Hi - I was looking for some trout today and found a river with lots of
big carps swimming around the edges.

I only had a rapala lure with me - unfortunately a floating one that I couldn't get deep enough to were the carps were sitting.

Wondering if its possible at all to catch a carp with such a lure?

How would you normally go about catching them?

Slide a snap-swivel onto your line with the snap part hanging down. Slide a bead on next then tie the end of the line to another snap-swivel with a barrel knot. Put a 12 inch leader on a good sized hook (#2). Put your weight on the swivel hanging on the line and your hook on the swivel tied to your line. I use Coon Shrimp for bait and secure them to the hook with magic string it is just strechy string small elastic string will work. They also bite on squid and herring. Experiment they are picky. Oh, when they bite they usually just nibble a little at first just wait a second or two till you set the hook or you will miss them. Hope this helps. Good fishing.