The various tools within the RCE (Rich Content Editor) of Canvas do not allow you to record your screen. However, if your school has purchased an add-on product from Instructure (the company that makes Canvas) called "Canvas Studio" (What is Canvas Studio?)
Studio does allow you to do screen recordings. You would know if your school has Studio or not because there would be a "Studio" button located on the left-hand side global navigation bar within Canvas. See How do I access Canvas Studio? for more information.
Do you have a smartphone or mobile tablet device? For example, both the iPhone and iPad have a screen recorder that you could possibly use for your assignment. Of course, you'd be dealing with a smaller screen, and I'm not sure that it records audio (if needed)...just video. How to record the screen on your iPhone, iPad, or iPod touch
I hope this will be of help to you in some way. Please let Community members know if you have any other questions about this...thanks!