diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index ea6a832d25058..4acfc1470a82f 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -757,6 +757,7 @@ Performance improvements
 - Performance improvement in :meth:`MultiIndex.putmask` (:issue:`49830`)
 - Performance improvement in :meth:`Index.union` and :meth:`MultiIndex.union` when index contains duplicates (:issue:`48900`)
 - Performance improvement in :meth:`Series.rank` for pyarrow-backed dtypes (:issue:`50264`)
+- Performance improvement in :meth:`Series.searchsorted` for pyarrow-backed dtypes (:issue:`50447`)
 - Performance improvement in :meth:`Series.fillna` for extension array dtypes (:issue:`49722`, :issue:`50078`)
 - Performance improvement in :meth:`Index.join`, :meth:`Index.intersection` and :meth:`Index.union` for masked dtypes when :class:`Index` is monotonic (:issue:`50310`)
 - Performance improvement for :meth:`Series.value_counts` with nullable dtype (:issue:`48338`)
diff --git a/pandas/core/arrays/arrow/array.py b/pandas/core/arrays/arrow/array.py
index d0c17161dea0b..de85ed67e7e8c 100644
--- a/pandas/core/arrays/arrow/array.py
+++ b/pandas/core/arrays/arrow/array.py
@@ -3,6 +3,7 @@
 from typing import (
     TYPE_CHECKING,
     Any,
+    Literal,
     TypeVar,
     cast,
 )
@@ -116,6 +117,11 @@ def floordiv_compat(
     }
 
 if TYPE_CHECKING:
+    from pandas._typing import (
+        NumpySorter,
+        NumpyValueArrayLike,
+    )
+
     from pandas import Series
 
 ArrowExtensionArrayT = TypeVar("ArrowExtensionArrayT", bound="ArrowExtensionArray")
@@ -693,6 +699,23 @@ def round(
         """
         return type(self)(pc.round(self._data, ndigits=decimals))
 
+    @doc(ExtensionArray.searchsorted)
+    def searchsorted(
+        self,
+        value: NumpyValueArrayLike | ExtensionArray,
+        side: Literal["left", "right"] = "left",
+        sorter: NumpySorter = None,
+    ) -> npt.NDArray[np.intp] | np.intp:
+        if self._hasna:
+            raise ValueError(
+                "searchsorted requires array to be sorted, which is impossible "
+                "with NAs present."
+            )
+        if isinstance(value, ExtensionArray):
+            value = value.astype(object)
+        # Base class searchsorted would cast to object, which is *much* slower.
+        return self.to_numpy().searchsorted(value, side=side, sorter=sorter)
+
     def take(
         self,
         indices: TakeIndexer,
diff --git a/pandas/core/arrays/string_.py b/pandas/core/arrays/string_.py
index e5fb3fc3ff836..9b26db07fc28f 100644
--- a/pandas/core/arrays/string_.py
+++ b/pandas/core/arrays/string_.py
@@ -1,6 +1,9 @@
 from __future__ import annotations
 
-from typing import TYPE_CHECKING
+from typing import (
+    TYPE_CHECKING,
+    Literal,
+)
 
 import numpy as np
 
@@ -54,6 +57,11 @@
 if TYPE_CHECKING:
     import pyarrow
 
+    from pandas._typing import (
+        NumpySorter,
+        NumpyValueArrayLike,
+    )
+
     from pandas import Series
 
 
@@ -492,6 +500,20 @@ def memory_usage(self, deep: bool = False) -> int:
             return result + lib.memory_usage_of_objects(self._ndarray)
         return result
 
+    @doc(ExtensionArray.searchsorted)
+    def searchsorted(
+        self,
+        value: NumpyValueArrayLike | ExtensionArray,
+        side: Literal["left", "right"] = "left",
+        sorter: NumpySorter = None,
+    ) -> npt.NDArray[np.intp] | np.intp:
+        if self._hasna:
+            raise ValueError(
+                "searchsorted requires array to be sorted, which is impossible "
+                "with NAs present."
+            )
+        return super().searchsorted(value=value, side=side, sorter=sorter)
+
     def _cmp_method(self, other, op):
         from pandas.arrays import BooleanArray
 
diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index c1785591f41a9..02f72d67673ae 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -1553,3 +1553,20 @@ def test_round():
     result = ser.round(-1)
     expected = pd.Series([120.0, pd.NA, 60.0], dtype=dtype)
     tm.assert_series_equal(result, expected)
+
+
+def test_searchsorted_with_na_raises(data_for_sorting, as_series):
+    # GH50447
+    b, c, a = data_for_sorting
+    arr = data_for_sorting.take([2, 0, 1])  # to get [a, b, c]
+    arr[-1] = pd.NA
+
+    if as_series:
+        arr = pd.Series(arr)
+
+    msg = (
+        "searchsorted requires array to be sorted, "
+        "which is impossible with NAs present."
+    )
+    with pytest.raises(ValueError, match=msg):
+        arr.searchsorted(b)
diff --git a/pandas/tests/extension/test_string.py b/pandas/tests/extension/test_string.py
index de7967a8578b5..3e865947aa968 100644
--- a/pandas/tests/extension/test_string.py
+++ b/pandas/tests/extension/test_string.py
@@ -420,3 +420,20 @@ def arrow_not_supported(self, data, request):
                 reason="2D support not implemented for ArrowStringArray"
             )
             request.node.add_marker(mark)
+
+
+def test_searchsorted_with_na_raises(data_for_sorting, as_series):
+    # GH50447
+    b, c, a = data_for_sorting
+    arr = data_for_sorting.take([2, 0, 1])  # to get [a, b, c]
+    arr[-1] = pd.NA
+
+    if as_series:
+        arr = pd.Series(arr)
+
+    msg = (
+        "searchsorted requires array to be sorted, "
+        "which is impossible with NAs present."
+    )
+    with pytest.raises(ValueError, match=msg):
+        arr.searchsorted(b)