Climbing Warmup Routine
I shamelessly stole this routine from a Louie Parkinson video, and modified it a bit. It's a three part warm up.
Part 1: Heart Rate
The first part is just to get your heart pumping so bloodflow is circulating. You can accomplish this by biking to the gym, doing jumping jacks, running in place, pushups, burpees, or any combination of those.
Part 2: Joints
Climbing requires some flexibility, so you need to loosen up your joints. I do some shoulder circles, straight-leg swings, wrist and ankle circles, and core twists.
Part 3: Technique Warmup
Now it's time to start climbing! Do some V0s, focus on your foot placements and keeping your arms and hands relaxed. I also tend to focus on twisting my hips so that I can reach the next hold with both of my arms straight.