diff --git a/cpp/src/arrow/dataset/file_test.cc b/cpp/src/arrow/dataset/file_test.cc
index 0c8954e6b7b..839b48a0e64 100644
--- a/cpp/src/arrow/dataset/file_test.cc
+++ b/cpp/src/arrow/dataset/file_test.cc
@@ -295,6 +295,49 @@ TEST_F(TestFileSystemDataset, FragmentPartitions) {
                 });
 }
 
+TEST_F(TestFileSystemDataset, WriteProjected) {
+  // Regression test for ARROW-12620
+  auto format = std::make_shared<IpcFileFormat>();
+  auto fs = std::make_shared<fs::internal::MockFileSystem>(fs::kNoTime);
+  FileSystemDatasetWriteOptions write_options;
+  write_options.file_write_options = format->DefaultWriteOptions();
+  write_options.filesystem = fs;
+  write_options.base_dir = "root";
+  write_options.partitioning = std::make_shared<HivePartitioning>(schema({}));
+  write_options.basename_template = "{i}.feather";
+
+  auto dataset_schema = schema({field("a", int64())});
+  RecordBatchVector batches{
+      ConstantArrayGenerator::Zeroes(kRowsPerBatch, dataset_schema)};
+  ASSERT_EQ(0, batches[0]->column(0)->null_count());
+  auto dataset = std::make_shared<InMemoryDataset>(dataset_schema, batches);
+  ASSERT_OK_AND_ASSIGN(auto scanner_builder, dataset->NewScan());
+  ASSERT_OK(scanner_builder->Project(
+      {compute::call("add", {compute::field_ref("a"), compute::literal(1)})},
+      {"a_plus_one"}));
+  ASSERT_OK_AND_ASSIGN(auto scanner, scanner_builder->Finish());
+
+  ASSERT_OK(FileSystemDataset::Write(write_options, scanner));
+
+  ASSERT_OK_AND_ASSIGN(auto dataset_factory, FileSystemDatasetFactory::Make(
+                                                 fs, {"root/0.feather"}, format, {}));
+  ASSERT_OK_AND_ASSIGN(auto written_dataset, dataset_factory->Finish(FinishOptions{}));
+  auto expected_schema = schema({field("a_plus_one", int64())});
+  AssertSchemaEqual(*expected_schema, *written_dataset->schema());
+  ASSERT_OK_AND_ASSIGN(scanner_builder, written_dataset->NewScan());
+  ASSERT_OK_AND_ASSIGN(scanner, scanner_builder->Finish());
+  ASSERT_OK_AND_ASSIGN(auto table, scanner->ToTable());
+  auto col = table->column(0);
+  ASSERT_EQ(0, col->null_count());
+  for (auto chunk : col->chunks()) {
+    auto arr = std::dynamic_pointer_cast<Int64Array>(chunk);
+    for (auto val : *arr) {
+      ASSERT_TRUE(val.has_value());
+      ASSERT_EQ(1, *val);
+    }
+  }
+}
+
 // Tests of subtree pruning
 
 struct TestPathTree {
diff --git a/cpp/src/arrow/dataset/scanner_internal.h b/cpp/src/arrow/dataset/scanner_internal.h
index 56065d9983e..30fb4e07cef 100644
--- a/cpp/src/arrow/dataset/scanner_internal.h
+++ b/cpp/src/arrow/dataset/scanner_internal.h
@@ -169,11 +169,7 @@ class FilterAndProjectScanTask : public ScanTask {
           ARROW_ASSIGN_OR_RAISE(auto projected, FilterAndProjectBatch(batch));
           return visitor(projected);
         };
-    return task_->SafeExecute(executor).Then(
-        [this, filter_and_project_visitor](const RecordBatchVector& rbs) -> Status {
-          ARROW_ASSIGN_OR_RAISE(auto projected_it, ToFilteredAndProjectedIterator(rbs));
-          return projected_it.Visit(filter_and_project_visitor);
-        });
+    return task_->SafeVisit(executor, filter_and_project_visitor);
   }
 
  private: