No. 18" tires require 18" wheels. If you want to use a 20" rim, you will have to buy new 20" (expensive) tires. You can, however, go with a much wider tire with your existing 18" wheels if you watch the aspect ratio.
If, for example, your car has a P225 60R18 tire/wheel, can can correctly install a P235 55R18, or a P255 50R18.
Use this tire calculator to determine the right size tire for your car, in order to keep the speedo accurate.
Tire Size Calculator - tire & wheel plus sizing