Have a look at RotSprite.
RotSprite is a scaling and rotation algorithm for sprites developed by Xenowhirl. It produces far fewer artifacts than nearest-neighbor rotation algorithms, and like EPX, it does not introduce new colors into the image (unlike most interpolation systems).
The algorithm first scales the image to 8 times its original size with a modified Scale2× algorithm which treats similar (rather than identical) pixels as matches. It then calculates what rotation offset to use by favoring sampled points which are not boundary pixels. Next, the rotated image is created with a nearest-neighbor scaling and rotation algorithm that simultaneously shrinks the big image back to its original size and rotates the image. Finally, overlooked single-pixel details are restored if the corresponding pixel in the source image is different and the destination pixel has three identical neighbors.
You can either implement this algorithm yourself as part of your game's drawing code, or use it to create rotated assets beforehand. The pixel art tool Aseprite has integrated RotSprite as part of its sprite editor.
Also, have a look at this Unity forums thread on how to use RotSprite in Unity, as well as more general information about RotSprite.