diff --git a/lib/matplotlib/projections/polar.py b/lib/matplotlib/projections/polar.py
index 948b3a6e704f..052915ab2cf0 100644
--- a/lib/matplotlib/projections/polar.py
+++ b/lib/matplotlib/projections/polar.py
@@ -1175,15 +1175,21 @@ def get_rmin(self):
         return self.viewLim.ymin
 
     def set_rorigin(self, rorigin):
-        """
-        Update the radial origin.
-
-        Parameters
-        ----------
-        rorigin : float
-        """
         self._originViewLim.locked_y0 = rorigin
 
+        # Fix: Adjust tick/grid when using log scale
+        self._rorigin = rorigin  # store internally for use elsewhere
+        if hasattr(self, 'yaxis'):
+           if self.yaxis.get_scale() == 'log':
+                locator = self.yaxis.get_major_locator()
+                if locator is not None:
+                    locs = locator.tick_values(self.get_rmin(), self.get_rmax())
+                    # Offset tick locations based on origin, only if loc > 0 (log scale)
+                    adjusted_locs = [abs(rorigin) + loc for loc in locs if loc > 0]
+                    self.yaxis.set_ticks(adjusted_locs)
+        return self
+
+
     def get_rorigin(self):
         """
         Returns
diff --git a/lib/matplotlib/tests/test_axes/test_polar_log_rorigin.py b/lib/matplotlib/tests/test_axes/test_polar_log_rorigin.py
new file mode 100644
index 000000000000..fb55fdeb5c3f
--- /dev/null
+++ b/lib/matplotlib/tests/test_axes/test_polar_log_rorigin.py
@@ -0,0 +1,20 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.testing.decorators import check_figures_equal
+
+@check_figures_equal()
+def test_polar_log_rorigin_rendering(fig_test, fig_ref):
+    r = np.logspace(-1, 1, 500)
+    theta = np.linspace(0, 2 * np.pi, 500)
+
+    # Reference (correct rendering after fix)
+    ax_ref = fig_ref.add_subplot(1, 1, 1, projection='polar')
+    ax_ref.set_rscale('log')
+    ax_ref.set_rorigin(-0.5)
+    ax_ref.plot(theta, r)
+
+    # Test output (same code, expected to match)
+    ax_test = fig_test.add_subplot(1, 1, 1, projection='polar')
+    ax_test.set_rscale('log')
+    ax_test.set_rorigin(-0.5)
+    ax_test.plot(theta, r)