Yes you can weave rugs on a rigid-heddle loom! In this pattern support video for the Spring 2017 Weave-Along, I walk you through the techniques used to make the Simply Striped Rug from "Weaving Made Easy". Also covered is what makes a rug yarn different from other yarns.
Resources
Finishing Tips https://yarnworker.com/finishing-tips-for-rugs
Geeking Out: Rugs (blog post) https://yarnworker.com/geeking-out-rugs
Weaving Made Easy https://www.penguinrandomhouse.com/books/632028/weaving-made-easy-revised-and-updated-by-liz-gipson
YarnworkerU https://yarnworkeru.com