I believe anything that can hold your weight has the potential to work. ^^ (I'm not an expert or anything, though.) People have hanged themselves using ties, scarves, electric chords, etc. You'll need something stronger if you want to do full suspension rather than partial, though. In either case, it's best to obtain a rope if you can. Miscellaneous items have a higher tendency to break.
From a quick search, there is a case where a very young child was hanged with a jumping rope. I'm not sure if an adult would be able to achieve the same.
Please make sure to read plenty of different guides and threads before trying anything! You could end up injured instead of dying if you're not careful.
Edit: You could try to figure out what material your jumping rope is made of, whether it's hollow, and how thick it is to get an estimate of its strength.