[TST] Parse arrow_dtype as datetime index

pandas/tests/io/parser/test_parse_dates.py

@@ -13,9 +13,8 @@
 import numpy as np
 import pytest
 
-from pandas._config import using_string_dtype
-
 import pandas as pd
+import pandas._testing as tm
 from pandas import (
     DataFrame,
     DatetimeIndex,
@@ -24,10 +23,9 @@
     Series,
     Timestamp,
 )
-import pandas._testing as tm
+from pandas._config import using_string_dtype
 from pandas.core.indexes.datetimes import date_range
 from pandas.core.tools.datetimes import start_caching_at
-
 from pandas.io.parsers import read_csv
 
 pytestmark = pytest.mark.filterwarnings(
@@ -848,6 +846,34 @@ def test_parse_dates_arrow_engine(all_parsers):
     tm.assert_frame_equal(result, expected)
 
 
+def test_parse_dates_arrow_dtype_as_index(all_parsers):
+    # GH#57930
+    parser = all_parsers
+    data = """a,b
+2000-01-01 00:00:00,1
+2000-01-01 00:00:01,1"""
+
+    result = parser.read_csv(
+        StringIO(data),
+        parse_dates=["a"],
+        index_col="a",
+        dtype_backend="pyarrow",
+    )
+    expected = Series(
+        [1, 1],
+        name="b",
+        dtype="int64[pyarrow]",
+        index=Index(
+            [
+                Timestamp("2000-01-01 00:00:00"),
+                Timestamp("2000-01-01 00:00:01"),
+            ],
+            name="a",
+        ),
+    ).to_frame()
+    tm.assert_frame_equal(result, expected)
+
+
 @xfail_pyarrow  # object dtype index
 def test_from_csv_with_mixed_offsets(all_parsers):
     parser = all_parsers