diff --git a/doc/source/whatsnew/v1.5.0.rst b/doc/source/whatsnew/v1.5.0.rst
index 199a52f9d770f..ade1fbcba0c26 100644
--- a/doc/source/whatsnew/v1.5.0.rst
+++ b/doc/source/whatsnew/v1.5.0.rst
@@ -243,7 +243,8 @@ Other Deprecations
 - Deprecated treating float-dtype data as wall-times when passed with a timezone to :class:`Series` or :class:`DatetimeIndex` (:issue:`45573`)
 - Deprecated the behavior of :meth:`Series.fillna` and :meth:`DataFrame.fillna` with ``timedelta64[ns]`` dtype and incompatible fill value; in a future version this will cast to a common dtype (usually object) instead of raising, matching the behavior of other dtypes (:issue:`45746`)
 - Deprecated the ``warn`` parameter in :func:`infer_freq` (:issue:`45947`)
-
+- Deprecated allowing non-keyword arguments in :meth:`ExtensionArray.argsort` (:issue:`46134`)
+-
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_150.performance:
diff --git a/pandas/core/arrays/base.py b/pandas/core/arrays/base.py
index 7c0daeecafaf7..b18a963e0cbc2 100644
--- a/pandas/core/arrays/base.py
+++ b/pandas/core/arrays/base.py
@@ -43,6 +43,7 @@
     Appender,
     Substitution,
     cache_readonly,
+    deprecate_nonkeyword_arguments,
 )
 from pandas.util._validators import (
     validate_bool_kwarg,
@@ -642,6 +643,7 @@ def _values_for_argsort(self) -> np.ndarray:
         # Note: this is used in `ExtensionArray.argsort/argmin/argmax`.
         return np.array(self)
 
+    @deprecate_nonkeyword_arguments(version=None, allowed_args=["self"])
     def argsort(
         self,
         ascending: bool = True,
diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index 3d9d3ef8a2557..db68eac504885 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -45,6 +45,7 @@
 from pandas.util._decorators import (
     cache_readonly,
     deprecate_kwarg,
+    deprecate_nonkeyword_arguments,
 )
 from pandas.util._exceptions import find_stack_level
 from pandas.util._validators import validate_bool_kwarg
@@ -1716,6 +1717,7 @@ def check_for_ordered(self, op):
                 "Categorical to an ordered one\n"
             )
 
+    @deprecate_nonkeyword_arguments(version=None, allowed_args=["self"])
     def argsort(self, ascending=True, kind="quicksort", **kwargs):
         """
         Return the indices that would sort the Categorical.
diff --git a/pandas/core/arrays/interval.py b/pandas/core/arrays/interval.py
index d23910c37b52b..2098dface40f6 100644
--- a/pandas/core/arrays/interval.py
+++ b/pandas/core/arrays/interval.py
@@ -37,7 +37,10 @@
 )
 from pandas.compat.numpy import function as nv
 from pandas.errors import IntCastingNaNError
-from pandas.util._decorators import Appender
+from pandas.util._decorators import (
+    Appender,
+    deprecate_nonkeyword_arguments,
+)
 
 from pandas.core.dtypes.cast import LossySetitemError
 from pandas.core.dtypes.common import (
@@ -776,6 +779,7 @@ def __lt__(self, other):
     def __le__(self, other):
         return self._cmp_method(other, operator.le)
 
+    @deprecate_nonkeyword_arguments(version=None, allowed_args=["self"])
     def argsort(
         self,
         ascending: bool = True,