@casey - Yes definitely! You can simply select the experiment you want to move, click the duplicate button, and then choose the project where you want to move the experiment to. You will need to delete the project from it's initial home if you don't want to see it in both places.
Here's a great article that explains this with some helpful images: https://learn.optimizely.com/hc/en-us/articles/201
@Amanda - Duplicating the experiment to another project is not the same as moving the experiment. When you do it the way to say it, you will lose the results and have to replace the experiment ID's in Integration programs like Google Universal Analytics.
Is there a way to move the experiment without losing the results and changing the ID?