Can I run Romex in a garage if the walls are not covered with drywall?

Yes, in most cases. NM cable (Romex) is permitted in one and two family dwellings and their attached or detached garages under NEC 2023 334.10. Nothing in the code requires the cable to be buried inside a finished wall. What changes on open stud walls is that the run is now exposed work, and 334.15 sets the rules.

What 334.15 requires

Exposed NM cable must closely follow the surface of the building finish or running boards per 334.15(A). That means stapling neatly along studs and plates, not draping cable across open air from truss to truss. Where the cable could be subject to physical damage, 334.15(B) requires protection with conduit, EMT, Schedule 80 PVC, guard strips, or other approved means. The classic example is the section of wall behind a parked truck or next to a workbench where things get leaned and slammed.

Where inspectors draw the line

Physical damage is a judgment call that belongs to the AHJ, but the common flags are: cable run horizontally across the face of studs below about 8 ft in a garage work area, cable crossing a garage door track zone, and cable on the wall surface near floor level. Running through bored holes in the center of studs, or up high along the top plate, almost always passes. Keep holes at least 1 1/4 in from the stud edge or add nail plates per 300.4(A).

Practical layout that passes

Drill the studs and run through the framing where you can. Where you must run vertically down to a box, stapling within 12 in of the box and every 4 1/2 ft per 334.30 keeps it legal. If the garage will ever get drywall, nothing changes; the same runs simply become concealed work. If the space is used as a real shop with material handling, skip the debate and sleeve the exposed drops in EMT.