Is there any sense in saying that circularly polarized EM waves have angular momentum?
Yes. Electromagnetic waves carry energy and momentum, and can carry angular momentum.
A linearly polarized wave packet doesn't carry any angular momentum (measured about an axis through its center -- a linearly polarized wave packet moving past you off to one side has angular momentum about an axis located where you are, just as a baseball flying past you does.)
A circularly polarized wave packet does carry angular momentum about its center ("spin" as opposed to "orbital" angular momentum, roughly).
Griffiths's book Introduction to Electrodynamics is a good place to learn about this at the advanced-undergraduate level.