WHO IS THIS OBSESSED?

It's only been a month since she bought it and Taylor Swift's Rhode Island pad is already attracting the crazies!

An obsessed fan was arrested near the singer's Rhode Island beach home early yesterday morning after allegedly SWIMMING up to her pad.  

Here's the back story -- around 2:20 AM, cops spotted the man getting out of the ocean, around 1 mile from Swift's home. Cops approached the guy and asked him what he was doing in the water -- and the man allegedly told police he had just completed a swim, in which he intended to meet Taylor. 

Sources say ... the man told cops he swam all the way to Swift's beach, but saw her security team ... and decided to swim back to where he came from (roughly 2 miles round trip in cold water).

The man was hauled to a nearby police station where he was booked for trespassing . He's still in custody and is to appear in court on May 24.