Absolutely not! The only thing that needs to be flexible is your mind.
One of the goals of yoga practice is to increase one's flexibility, therefore you do not need to be flexible as a prerequisite to doing yoga.
Yoga poses are designed to expose blocks and imbalances in the body. After just a little bit of yoga much of the tension in your muscles will release and your range of motion will naturally increase.
If you feel you're inflexible a good place to start is with one of our beginner programs:
Yoga 101 - for absolute beginners
Beginner's Journey Program - 14 classes to learn the basics and beyond
Or try one of these classes from our Yoga for Flexibility section: