The issue, as others have noted, is a type of texture bleeding. I don't know the full technical reasons behind it but I know that it's worsened by precision problems. That is to say, it's worse on an angle of 12.019228 than 12.00000, which is worse than 10 or 15. However it doesn't affect all things equally either, as your bow is affected but other sprites may not be.
A solution could be to make a new sprite that is already rotated, but you may also be able to find a scale/rotation that doesn't cause the effect.