From delta.com:
What Instruments Can I Carry On?
Guitars and other smaller musical instruments, such as violins, will be accepted as your free carry-on baggage item on Delta and Delta Connection® carriers flightsą. These items must easily fit in the overhead bin or other approved storage location in the cabin, based on available space at the time of boarding. Musical instruments may be gate claimed at the discretion of the passenger and as a result of limited overhead space.
IIRC the instrument can exceed the standard 45" L+W+H limit that applies to all other carry-on items, but it must fit in the overhead bin.