Fix scatter norm keyword

pandas/plotting/_matplotlib/core.py

@@ -1082,7 +1082,7 @@ def _make_plot(self):
             bounds = np.linspace(0, n_cats, n_cats + 1)
             norm = colors.BoundaryNorm(bounds, cmap.N)
         else:
-            norm = None
+            norm = self.kwds.pop("norm", None)
         # plot colorbar if
         # 1. colormap is assigned, and
         # 2.`c` is a column containing only numeric values

pandas/tests/plotting/frame/test_frame.py

@@ -787,6 +787,18 @@ def test_plot_scatter_with_s(self):
         ax = df.plot.scatter(x="a", y="b", s="c")
         tm.assert_numpy_array_equal(df["c"].values, right=ax.collections[0].get_sizes())
 
+    def test_plot_scatter_with_norm(self):
+        # added while fixing GH 45809
+        import matplotlib as mpl
+
+        ax = self.hexbin_df.plot.scatter(x="A", y="B", c="C", norm=mpl.colors.LogNorm())
+        assert ax.collections[0].norm._scale
+
+    def test_plot_scatter_without_norm(self):
+        # added while fixing GH 45809
+        ax = self.hexbin_df.plot.scatter(x="A", y="B", c="C")
+        assert ax.collections[0].norm._scale is None
+
     def test_plot_bar(self):
         df = DataFrame(
             np.random.randn(6, 4),