diff --git a/doc/whats_new/v1.6.rst b/doc/whats_new/v1.6.rst
index 87814e102ad98..060ebca31722f 100644
--- a/doc/whats_new/v1.6.rst
+++ b/doc/whats_new/v1.6.rst
@@ -80,6 +80,13 @@ Changelog
 - |Enhancement| Added a function :func:`base.is_clusterer` which determines
   whether a given estimator is of category clusterer.
   :pr:`28936` by :user:`Christian Veenhuis <ChVeen>`.
+
+:mod:`sklearn.linear_model`
+...........................
+
+- |API| Deprecates `copy_X` in :class:`linear_model.TheilSenRegressor` as the parameter
+  has no effect. `copy_X` will be removed in 1.8.
+  :pr:`29105` by :user:`Adam Li <adam2392>`.
   
 :mod:`sklearn.metrics`
 ......................
diff --git a/sklearn/linear_model/_theil_sen.py b/sklearn/linear_model/_theil_sen.py
index cc774e8783762..b1ebd6524cb27 100644
--- a/sklearn/linear_model/_theil_sen.py
+++ b/sklearn/linear_model/_theil_sen.py
@@ -20,7 +20,7 @@
 from ..base import RegressorMixin, _fit_context
 from ..exceptions import ConvergenceWarning
 from ..utils import check_random_state
-from ..utils._param_validation import Interval
+from ..utils._param_validation import Hidden, Interval, StrOptions
 from ..utils.parallel import Parallel, delayed
 from ._base import LinearModel
 
@@ -228,6 +228,10 @@ class TheilSenRegressor(RegressorMixin, LinearModel):
     copy_X : bool, default=True
         If True, X will be copied; else, it may be overwritten.
 
+        .. deprecated:: 1.6
+            `copy_X` was deprecated in 1.6 and will be removed in 1.8.
+            It has no effect as a copy is always made.
+
     max_subpopulation : int, default=1e4
         Instead of computing with a set of cardinality 'n choose k', where n is
         the number of samples and k is the number of subsamples (at least
@@ -324,7 +328,7 @@ class TheilSenRegressor(RegressorMixin, LinearModel):
 
     _parameter_constraints: dict = {
         "fit_intercept": ["boolean"],
-        "copy_X": ["boolean"],
+        "copy_X": ["boolean", Hidden(StrOptions({"deprecated"}))],
         # target_type should be Integral but can accept Real for backward compatibility
         "max_subpopulation": [Interval(Real, 1, None, closed="left")],
         "n_subsamples": [None, Integral],
@@ -339,7 +343,7 @@ def __init__(
         self,
         *,
         fit_intercept=True,
-        copy_X=True,
+        copy_X="deprecated",
         max_subpopulation=1e4,
         n_subsamples=None,
         max_iter=300,
@@ -411,6 +415,14 @@ def fit(self, X, y):
         self : returns an instance of self.
             Fitted `TheilSenRegressor` estimator.
         """
+        if self.copy_X != "deprecated":
+            warnings.warn(
+                "`copy_X` was deprecated in 1.6 and will be removed in 1.8 since it "
+                "has no effect internally. Simply leave this parameter to its default "
+                "value to avoid this warning.",
+                FutureWarning,
+            )
+
         random_state = check_random_state(self.random_state)
         X, y = self._validate_data(X, y, y_numeric=True)
         n_samples, n_features = X.shape
diff --git a/sklearn/linear_model/tests/test_theil_sen.py b/sklearn/linear_model/tests/test_theil_sen.py
index c8415d02be80a..f72c18c24a809 100644
--- a/sklearn/linear_model/tests/test_theil_sen.py
+++ b/sklearn/linear_model/tests/test_theil_sen.py
@@ -292,3 +292,11 @@ def test_less_samples_than_features():
     theil_sen = TheilSenRegressor(fit_intercept=True, random_state=0).fit(X, y)
     y_pred = theil_sen.predict(X)
     assert_array_almost_equal(y_pred, y, 12)
+
+
+# TODO(1.8): Remove
+def test_copy_X_deprecated():
+    X, y, _, _ = gen_toy_problem_1d()
+    theil_sen = TheilSenRegressor(copy_X=True, random_state=0)
+    with pytest.warns(FutureWarning, match="`copy_X` was deprecated"):
+        theil_sen.fit(X, y)