Can I patch a leaky windshield with caulk? Tips and suggestions?

1991 Subaru Legacy. When it rains, water drains in from the top of my windshield, pooling and dripping down onto the steering wheel and passenger side. I want to avoid replacing entire windshield if possible, since it is undamaged. Is there a liquid caulk I can squeeze around the rim to prevent moisture getting in? Any application tips?