For enlisted, no. It was just joining the Navy.
For officers, since there was a rapid increase in officer posts, a volunteer officer system was created. A civilian/merchant ship commander, mate, pilot, engineer, or other specialized position could apply for a volunteer berth. The "permanent" Navy ranks always outranked the equivalent "volunteer" ranks. The vast majority of these were in the lower ranks such as Ensign and Lieutenant. A very few Acting Volunteer Lieutenants were advanced to Acting Volunteer Lieutenant Commander by the end of the war. Volunteer commissions were for the duration of the war, although permanent berths were offered to a limited number of deserving (and willing) volunteer officers after the conflict ended.
To give an idea of scope, here are the numbers of line officers by rank according to the 1864 Navy Register (quick count, might be a few off here and there on the larger lists):
Rear Admirals: Active 6, Retired 8
Commodores: Active 18, Retired 31
Captains: Active 36, Retired 14, Reserved 10
Commanders: Active 72, Retired 7, Reserved 15
Lieutenant Commanders (all active): 144
Lieutenants: Active 96, Retired 8, Reserved 9; Acting Volunteer Lieutenants 81
Masters: Reserved 2; Acting Masters 509
Ensigns: Active 58, Reserved 33, Acting Volunteer Ensign approx 700
Midshipmen: Active 2 (this rank was being discontinued in favor of Ensign)
In terms of warrant or specialty positions, there were also Acting Volunteer Master's Mates, Assistant Surgeons, Assistant Paymasters, Engineers, Boatswains, Gunners, and Carpenters.
"Retired" and "Reserved" did not necessarily mean the officer was unemployed; at the peak of the war, many were in shore administrative positions and other places where they could free up an active-duty officer for service elsewhere. (For instance, Retired Rear Admiral Francis Gregory had a supervisory position in the production of Union ironclads.)