diff --git a/RELEASE-NOTES.md b/RELEASE-NOTES.md
index 2dd70fbaf4..91227e409d 100644
--- a/RELEASE-NOTES.md
+++ b/RELEASE-NOTES.md
@@ -46,6 +46,7 @@ This new version of `Theano-PyMC` comes with an experimental JAX backend which,
 - Test model logp before starting any MCMC chains (see [#4116](https://github.com/pymc-devs/pymc3/issues/4116))
 - Fix bug in `model.check_test_point` that caused the `test_point` argument to be ignored. (see [PR #4211](https://github.com/pymc-devs/pymc3/pull/4211#issuecomment-727142721))
 - Refactored MvNormal.random method with better handling of sample, batch and event shapes. [#4207](https://github.com/pymc-devs/pymc3/pull/4207)
+- The `InverseGamma` distribution now implements a `logcdf`. [#3944](https://github.com/pymc-devs/pymc3/pull/3944)
 
 ### Documentation
 - Added a new notebook demonstrating how to incorporate sampling from a conjugate Dirichlet-multinomial posterior density in conjunction with other step methods (see [#4199](https://github.com/pymc-devs/pymc3/pull/4199)).
diff --git a/pymc3/distributions/continuous.py b/pymc3/distributions/continuous.py
index 234d5d7aed..533aeff5b4 100644
--- a/pymc3/distributions/continuous.py
+++ b/pymc3/distributions/continuous.py
@@ -2634,6 +2634,30 @@ def logp(self, value):
     def _distr_parameters_for_repr(self):
         return ["alpha", "beta"]
 
+    def logcdf(self, value):
+        """
+        Compute the log of the cumulative distribution function for Inverse Gamma distribution
+        at the specified value.
+
+        Parameters
+        ----------
+        value: numeric
+            Value(s) for which log CDF is calculated. If the log CDF for multiple
+            values are desired the values must be provided in a numpy array or theano tensor.
+
+        Returns
+        -------
+        TensorVariable
+        """
+        alpha = self.alpha
+        beta = self.beta
+        return bound(
+            tt.log(tt.gammaincc(alpha, beta / value)),
+            value >= 0,
+            alpha > 0,
+            beta > 0,
+        )
+
 
 class ChiSquared(Gamma):
     r"""
diff --git a/pymc3/tests/test_distributions.py b/pymc3/tests/test_distributions.py
index 6a2593ac97..04d9b0e3c0 100644
--- a/pymc3/tests/test_distributions.py
+++ b/pymc3/tests/test_distributions.py
@@ -913,6 +913,10 @@ def test_fun(value, mu, sigma):
             lambda value, alpha, beta: sp.gamma.logcdf(value, alpha, scale=1.0 / beta),
         )
 
+    @pytest.mark.xfail(
+        condition=(theano.config.floatX == "float32"),
+        reason="Fails on float32 due to numerical issues",
+    )
     def test_inverse_gamma(self):
         self.pymc3_matches_scipy(
             InverseGamma,
@@ -920,6 +924,12 @@ def test_inverse_gamma(self):
             {"alpha": Rplus, "beta": Rplus},
             lambda value, alpha, beta: sp.invgamma.logpdf(value, alpha, scale=beta),
         )
+        self.check_logcdf(
+            InverseGamma,
+            Rplus,
+            {"alpha": Rplus, "beta": Rplus},
+            lambda value, alpha, beta: sp.invgamma.logcdf(value, alpha, scale=beta),
+        )
 
     @pytest.mark.xfail(
         condition=(theano.config.floatX == "float32"),