Start with the smallest steps possible. Maybe that means opening the assignment and saving it to your computer. Then put it down and walk away. Come back in a little while and take another small step, such as reading over the assignment or making an outline of what you need to do to get it done. Often once you've done something you will often start to feel a lot different than if you've done nothing.
Keep track of how you're feeling. It's okay to feel more anxiety at first because you're doing something instead of nothing. Those feelings tend to subside over time as you take action, but the point is not to reduce your anxiety, the point is that you are making a commitment to do something in your life, to live your life, rather than to remain paralyzed in fear. Your goal is not to get rid of the anxiety but to live the kind of life you want to live.
This is the model for Acceptance and Commitment Therapy. A great book on this is "Get Out of Your Mind and into Your Life."