Has this happened a bunch of times?
Off the top of my head, it sounds like wind and current are in opposite directions - current pushes the boat towards the wind and as it does so the exposed windage gets larger and larger. At some point it reaches equilibrium where they are exerting an equal force on the boat, and there you sit with your beam to the wind. The usual complaint about fin keeled boats at anchor (without current) is that they tend to "sail around" a bit and won't stay in one place.