diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index f50442eb7ca46..d6d3127e67945 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -626,6 +626,7 @@ Datetimelike
 - Bug in adding a ``np.timedelta64`` object to a :class:`BusinessDay` or :class:`CustomBusinessDay` object incorrectly raising (:issue:`44532`)
 - Bug in :meth:`Index.insert` for inserting ``np.datetime64``, ``np.timedelta64`` or ``tuple`` into :class:`Index` with ``dtype='object'`` with negative loc adding ``None`` and replacing existing value (:issue:`44509`)
 - Bug in :meth:`Series.mode` with ``DatetimeTZDtype`` incorrectly returning timezone-naive and ``PeriodDtype`` incorrectly raising (:issue:`41927`)
+- Bug in :class:`DateOffset`` addition with :class:`Timestamp` where ``offset.nanoseconds`` would not be included in the result. (:issue:`43968`)
 -
 
 Timedelta
diff --git a/pandas/_libs/tslibs/offsets.pyx b/pandas/_libs/tslibs/offsets.pyx
index 7e6d8fa38aa45..6df4abc160b0b 100644
--- a/pandas/_libs/tslibs/offsets.pyx
+++ b/pandas/_libs/tslibs/offsets.pyx
@@ -186,8 +186,9 @@ def apply_wraps(func):
         if self.normalize:
             result = result.normalize()
 
-        # nanosecond may be deleted depending on offset process
-        if not self.normalize and nano != 0:
+        # If the offset object does not have a nanoseconds component,
+        # the result's nanosecond component may be lost.
+        if not self.normalize and nano != 0 and not hasattr(self, "nanoseconds"):
             if result.nanosecond != nano:
                 if result.tz is not None:
                     # convert to UTC
@@ -333,7 +334,7 @@ cdef _determine_offset(kwds):
             # sub-daily offset - use timedelta (tz-aware)
             offset = timedelta(**kwds_no_nanos)
     else:
-        offset = timedelta(1)
+        offset = timedelta(0)
     return offset, use_relativedelta
 
 
@@ -1068,12 +1069,17 @@ cdef class RelativeDeltaOffset(BaseOffset):
                 # perform calculation in UTC
                 other = other.replace(tzinfo=None)
 
+            if hasattr(self, "nanoseconds"):
+                td_nano = Timedelta(nanoseconds=self.nanoseconds)
+            else:
+                td_nano = Timedelta(0)
+
             if self.n > 0:
                 for i in range(self.n):
-                    other = other + self._offset
+                    other = other + self._offset + td_nano
             else:
                 for i in range(-self.n):
-                    other = other - self._offset
+                    other = other - self._offset - td_nano
 
             if tzinfo is not None and self._use_relativedelta:
                 # bring tz back from UTC calculation
diff --git a/pandas/_libs/tslibs/timestamps.pyx b/pandas/_libs/tslibs/timestamps.pyx
index f491b5aeedadc..1c26793876e5a 100644
--- a/pandas/_libs/tslibs/timestamps.pyx
+++ b/pandas/_libs/tslibs/timestamps.pyx
@@ -307,7 +307,6 @@ cdef class _Timestamp(ABCTimestamp):
         elif not isinstance(self, _Timestamp):
             # cython semantics, args have been switched and this is __radd__
             return other.__add__(self)
-
         return NotImplemented
 
     def __sub__(self, other):
diff --git a/pandas/tests/tseries/offsets/test_offsets.py b/pandas/tests/tseries/offsets/test_offsets.py
index 6cec35939dff2..5dcfd0019e93f 100644
--- a/pandas/tests/tseries/offsets/test_offsets.py
+++ b/pandas/tests/tseries/offsets/test_offsets.py
@@ -668,14 +668,6 @@ def test_rule_code(self):
                 assert alias == (_get_offset(alias) * 5).rule_code
 
 
-def test_dateoffset_misc():
-    oset = offsets.DateOffset(months=2, days=4)
-    # it works
-    oset.freqstr
-
-    assert not offsets.DateOffset(months=2) == 2
-
-
 def test_freq_offsets():
     off = BDay(1, offset=timedelta(0, 1800))
     assert off.freqstr == "B+30Min"
@@ -791,6 +783,54 @@ def test_tick_normalize_raises(tick_classes):
         cls(n=3, normalize=True)
 
 
+@pytest.mark.parametrize(
+    "offset_kwargs, expected_arg",
+    [
+        ({"nanoseconds": 1}, "1970-01-01 00:00:00.000000001"),
+        ({"nanoseconds": 5}, "1970-01-01 00:00:00.000000005"),
+        ({"nanoseconds": -1}, "1969-12-31 23:59:59.999999999"),
+        ({"microseconds": 1}, "1970-01-01 00:00:00.000001"),
+        ({"microseconds": -1}, "1969-12-31 23:59:59.999999"),
+        ({"seconds": 1}, "1970-01-01 00:00:01"),
+        ({"seconds": -1}, "1969-12-31 23:59:59"),
+        ({"minutes": 1}, "1970-01-01 00:01:00"),
+        ({"minutes": -1}, "1969-12-31 23:59:00"),
+        ({"hours": 1}, "1970-01-01 01:00:00"),
+        ({"hours": -1}, "1969-12-31 23:00:00"),
+        ({"days": 1}, "1970-01-02 00:00:00"),
+        ({"days": -1}, "1969-12-31 00:00:00"),
+        ({"weeks": 1}, "1970-01-08 00:00:00"),
+        ({"weeks": -1}, "1969-12-25 00:00:00"),
+        ({"months": 1}, "1970-02-01 00:00:00"),
+        ({"months": -1}, "1969-12-01 00:00:00"),
+        ({"years": 1}, "1971-01-01 00:00:00"),
+        ({"years": -1}, "1969-01-01 00:00:00"),
+    ],
+)
+def test_dateoffset_add_sub(offset_kwargs, expected_arg):
+    offset = DateOffset(**offset_kwargs)
+    ts = Timestamp(0)
+    result = ts + offset
+    expected = Timestamp(expected_arg)
+    assert result == expected
+    result -= offset
+    assert result == ts
+    result = offset + ts
+    assert result == expected
+
+
+def test_dataoffset_add_sub_timestamp_with_nano():
+    offset = DateOffset(minutes=2, nanoseconds=9)
+    ts = Timestamp(4)
+    result = ts + offset
+    expected = Timestamp("1970-01-01 00:02:00.000000013")
+    assert result == expected
+    result -= offset
+    assert result == ts
+    result = offset + ts
+    assert result == expected
+
+
 @pytest.mark.parametrize(
     "attribute",
     [
@@ -806,3 +846,11 @@ def test_dateoffset_immutable(attribute):
     msg = "DateOffset objects are immutable"
     with pytest.raises(AttributeError, match=msg):
         setattr(offset, attribute, 5)
+
+
+def test_dateoffset_misc():
+    oset = offsets.DateOffset(months=2, days=4)
+    # it works
+    oset.freqstr
+
+    assert not offsets.DateOffset(months=2) == 2