Fill the birdbath with water. Inspect the bottom to find the highest point the water is leaking from. Compare the location of the wet spot to the inside of the bowl. Look for a crack that may extend even farther up the interior.
Empty the water from the birdbath. If necessary, wash the bath with soapy water to get rid of scum and let it dry thoroughly.
Clean out the crack with a screwdriver, chisel or grinding tool if it's wider than a hairline crack. Remove any loose concrete, dig down to firm concrete and widen the bottom of the crack slightly so it's at least as wide at the bottom as the top, to give a good surface for the patching material to grip. Blow out any debris.
Mix epoxy concrete patching compound according to the label directions. With a putty knife, press the compound into the crack and smooth the excess to either side. Coat the interior of the birdbath with a thin layer of the compound to waterproof it, if you desire.
Let the epoxy dry for 24 hours or as long as the label suggests before refilling the birdbath.