Can fiber-optic data cable be run overhead to a garage?
Yes, absolutely.

The fiber you'll want for this job is "Drop" fiber - it's made to resemble (and work with the hardware for) telephone "drop" wire - and it's relatively inexpensive while being quite robust.



While we tend to knee-jerk away from aerial fiber because it's more exposed to damage, this is a perfectly viable solution.

However, for most home applications at this time, it's going to be much cheaper/easier and adequately effective (not really as fast as fiber, but probably faster than your internet feed unless you have gigabit fiber to your house) to use a 5 GHz "ac" "Point to Point" radio link between the buildings.