The Baltimore Oriole is a summer resident here. A
Yes, birds can carry ticks. But ticks are very "host-specific". So it's extremely unlikely that a bird-borne tick will latch onto a human, cat or dog. Also, birds groom themselves a lot and actually eat ticks.
If you like to be "one with nature" occasionally, you may pick up unwanted hitchhikers in the form of ticks. To rid yourself of the vast majority of them, try a lint roller - with wide tape. Unless they've dug in, it will collect them effectively.