Climbing can use muscles that you are not used to using on a regular basis. Even regular rock climbers know that stretching may give them an edge when it comes to surviving a climb. This makes stretching before a climb a mandatory exercise. While the body itself may be warm and ready to go, the muscles needed to complete a climb should be engaged prior to beginning an ascent; this makes warming them up worth the effort.
When it comes to warming up, there are a wide range of exercises to consider to prepare for a climb. The two best exercises are knee pull-ups and the flag and reach with some hip rotations. The arms and legs see a lot of use, and you want to be able to stretch as far as possible during the climb. You just can never be completely sure what you will need to do to get from one area to another. While you should do other exercises as well, these are the ones that get you in the best shape the fastest.
The knee pull-up entails bringing your knee as close to your chest as close as possible while standing and then repeating with the other knee. Make sure that you can feel the muscles stretching or this does little good. This stretch engages the leg muscles and gets them ready for a full day of climbing, especially when it comes to pushing off of rocks and allowing you to get into more areas.
The flag and reach mimics the action of stretching to plant a flag. While standing, reach as far up and to the side as you can; again, make sure you feel the muscles stretching and repeat on both sides. Your arms will be spending the entire day stretching, grabbing, and pulling, and this exercise gets them ready for exactly that.
These should be just the start. Hopefully, the walk to the climb site should help warm you up in general, but these stretches should help you get ready for the climb itself. You need every edge when it comes to climbing, and these should give you that edge.