Is this the flowering annual vinca (Catharanthus), sometimes also called Madagascar periwinkle? If so, it is propagated from seed. It may survive overwinter in a greenhouse or sunroom, but is not likely to survive as a regular houseplant.
Vinca vine (Vinca major) propagates readily from layering, where the vine touches the soil. It also does not make a good houseplant, but if it's not hardy in your area, could be grown in a greenhouse over winter.