diff --git a/pymc/distributions/multivariate.py b/pymc/distributions/multivariate.py
index f0f031ff02..96a91a336a 100644
--- a/pymc/distributions/multivariate.py
+++ b/pymc/distributions/multivariate.py
@@ -2115,6 +2115,13 @@ class CAR(Continuous):
     def dist(cls, mu, W, alpha, tau, *args, **kwargs):
         return super().dist([mu, W, alpha, tau], **kwargs)
 
+    def get_moment(rv, size, mu, W, alpha, tau):
+        moment = mu
+        if not rv_size_is_none(size):
+            moment_size = at.concatenate([size, moment.shape])
+            moment = at.full(moment_size, mu)
+        return moment
+
     def logp(value, mu, W, alpha, tau):
         """
         Calculate log-probability of a CAR-distributed vector
diff --git a/pymc/tests/test_distributions_moments.py b/pymc/tests/test_distributions_moments.py
index 4a6361504e..4471b5c5eb 100644
--- a/pymc/tests/test_distributions_moments.py
+++ b/pymc/tests/test_distributions_moments.py
@@ -9,6 +9,7 @@
 import pymc as pm
 
 from pymc.distributions import (
+    CAR,
     AsymmetricLaplace,
     Bernoulli,
     Beta,
@@ -109,7 +110,6 @@ def test_all_distributions_have_moments():
     # Distributions that have been refactored but don't yet have moments
     not_implemented |= {
         dist_module.discrete.DiscreteWeibull,
-        dist_module.multivariate.CAR,
         dist_module.multivariate.DirichletMultinomial,
         dist_module.multivariate.Wishart,
     }
@@ -932,6 +932,34 @@ def test_mv_normal_moment(mu, cov, size, expected):
     assert_moment_is_expected(model, expected, check_finite_logp=x.ndim < 3)
 
 
+@pytest.mark.parametrize(
+    "mu, size, expected",
+    [
+        (
+            np.array([1, 0, 3.0, 4]),
+            None,
+            np.array([1, 0, 3.0, 4]),
+        ),
+        (np.array([1, 0, 3.0, 4]), 6, np.full((6, 4), [1, 0, 3.0, 4])),
+        (np.array([1, 0, 3.0, 4]), (5, 3), np.full((5, 3, 4), [1, 0, 3.0, 4])),
+        (
+            np.array([[3.0, 5, 2, 1], [1, 4, 0.5, 9]]),
+            (4, 5),
+            np.full((4, 5, 2, 4), [[3.0, 5, 2, 1], [1, 4, 0.5, 9]]),
+        ),
+    ],
+)
+def test_car_moment(mu, size, expected):
+    W = np.array(
+        [[0.0, 1.0, 1.0, 0.0], [1.0, 0.0, 0.0, 1.0], [1.0, 0.0, 0.0, 1.0], [0.0, 1.0, 1.0, 0.0]]
+    )
+    tau = 2
+    alpha = 0.5
+    with Model() as model:
+        CAR("x", mu=mu, W=W, alpha=alpha, tau=tau, size=size)
+    assert_moment_is_expected(model, expected)
+
+
 @pytest.mark.parametrize(
     "mu, sigma, size, expected",
     [