diff --git a/DESCRIPTION b/DESCRIPTION
index 2f94c807..0848e656 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -15,7 +15,7 @@ BugReports: https://github.com/r-lib/httr/issues
 Depends:
     R (>= 3.5)
 Imports:
-    curl (>= 3.0.0),
+    curl (>= 5.0.2),
     jsonlite,
     mime,
     openssl (>= 0.8),
diff --git a/NEWS.md b/NEWS.md
index 32b59973..4180465c 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,5 +1,7 @@
 # httr 1.4.7
 
+* Add support for seeking in uploads (#741).
+
 * Suppress another use of httpbin.
 
 * More aggressively skip httpbin using tests.
diff --git a/R/body.R b/R/body.R
index f2499b5a..dd4d3ede 100644
--- a/R/body.R
+++ b/R/body.R
@@ -25,6 +25,12 @@ body_config <- function(body = NULL,
           }
           bin
         },
+        seekfunction = function(offset, ...) {
+          if (is.null(con)) {
+            con <<- file(body$path, "rb")
+          }
+          seek(con, where = offset)
+        },
         postfieldsize_large = size
       ),
       content_type(body$type)
diff --git a/tests/testthat/test-upload-file.R b/tests/testthat/test-upload-file.R
new file mode 100644
index 00000000..588ee548
--- /dev/null
+++ b/tests/testthat/test-upload-file.R
@@ -0,0 +1,17 @@
+test_that("can upload with redirect", {
+  skip_on_cran()
+
+  str <- paste(letters, collapse = '')
+  tmp <- tempfile()
+  writeBin(str, tmp)
+
+  resp <- PUT(
+    "https://hb.cran.dev/redirect-to?url=/put&status_code=307",
+    body = upload_file(tmp)
+  )
+
+  expect_equal(resp$status_code, 200)
+  expect_equal(resp$url, "https://hb.cran.dev/put")
+  json <- content(resp)
+  expect_equal(json$data, str)
+})