Let's assume you have your shapes distributed uniformly, for ex the spacing is 30 degrees. Let's assume one of the shapes has the wanted angle position, others need rotation. Then
Pick one shape, copy it to the clipboard, paste it elsewhere, select again your whole circular pattern, rotate it 30 degrees, pick the next shape and copy it to elsewhere, etc...
You can repeat the last rotation with Ctrl+D if you haven't rotated nor moved anything between. Scrolling the page forth and back to be able to paste elsewhere doesn't harm.Only remember to reselect the circular pattern.
Align your separated shapes vertically and distribute horizontally with the Align and Distribute panel.
If your shapes are non-uniformly distributed or need more complex than linearly cumulating rotations for some other reasons, the only way is to rotate them one by one, Illustrator doesn't know the right angles.