Any way to visibly improve anti-aliasing?

I want the lines in my project to look as sharp as possible. The most noticeable aliasing is coming from the player sprite, which is a 32x32 square. It rotates freely around, and these jagged edges are a bother.

The only thing I know that's related in C2 to aliasing is Point vs. Linear sampling. I can't even tell the difference because the sprite is so small. Is there anything I can do to improve the AA, or am I stuck with what I got because of the sprite size?

Don't forget to add 1px empty border around your sprite texture.

Thanks for the tip! That really helps.

Wish this could somehow work with shadows and lightcasting though.