diff --git a/cpp/src/arrow/compute/kernels/scalar_string.cc b/cpp/src/arrow/compute/kernels/scalar_string.cc
index be1cc83d158..65196b2a491 100644
--- a/cpp/src/arrow/compute/kernels/scalar_string.cc
+++ b/cpp/src/arrow/compute/kernels/scalar_string.cc
@@ -1332,7 +1332,7 @@ struct ReplaceSubString {
 
     if (batch[0].kind() == Datum::ARRAY) {
       // We already know how many strings we have, so we can use Reserve/UnsafeAppend
-      RETURN_NOT_OK(offset_builder.Reserve(batch[0].array()->length));
+      RETURN_NOT_OK(offset_builder.Reserve(batch[0].array()->length + 1));
       offset_builder.UnsafeAppend(0);  // offsets start at 0
 
       const ArrayData& input = *batch[0].array();
diff --git a/cpp/src/arrow/compute/kernels/scalar_string_test.cc b/cpp/src/arrow/compute/kernels/scalar_string_test.cc
index cb74b1449b5..a59634b7be8 100644
--- a/cpp/src/arrow/compute/kernels/scalar_string_test.cc
+++ b/cpp/src/arrow/compute/kernels/scalar_string_test.cc
@@ -499,6 +499,14 @@ TYPED_TEST(TestStringKernels, ReplaceSubstringRegex) {
   ReplaceSubstringOptions options_regex2{"(a.a)", "aba\\1"};
   this->CheckUnary("replace_substring_regex", R"(["aaaaaa"])", this->type(),
                    R"(["abaaaaabaaaa"])", &options_regex2);
+
+  // ARROW-12774
+  ReplaceSubstringOptions options_regex3{"X", "Y"};
+  this->CheckUnary("replace_substring_regex",
+                   R"(["A","A","A","A","A","A","A","A","A","A","A","A","A","A","A","A"])",
+                   this->type(),
+                   R"(["A","A","A","A","A","A","A","A","A","A","A","A","A","A","A","A"])",
+                   &options_regex3);
 }
 
 TYPED_TEST(TestStringKernels, ReplaceSubstringRegexLimited) {