It is possible to catch carp with hook and line. We used to catch them for fun when I was a kid. We would fish with medium to heavy spinning tackle depending upon the size.
Read up on some good doughball recipes. Chum your fishing area for a few days before you plan to fish.
Then chum it at about 50% when you sit down to fish.
Set the hook lightly compared to bass fishing. Make sure your drag is properly set - they will give you a great fight.
Catching carp was something that I'd do as a kid and it wasn't hard at all. Chum with whole kernel canned corn, then fill a #2 Aberdeen hook with corn, cast it out to the chummed area. No weight, no bobber, 8# test line. Leave a belly in the line. When the belly started to get tight, pick up the rod and set the hook.
Triploid Grass Carp on the other hand are a whole 'nother ball game!