I most certainly know what you're going through. This doesn't always happen to me, when usually when my anxiety is really bad, it is there to greet me in the morning. I have a few ideas for you.
You might try keeping a journal and pen near your bed. When you wake up in the morning and feel anxious, just write down at least three things that you are grateful for/happy about. This can help set the tone for a more positive day. You can also write down some positive affirmations to say to yourself in the mirror in the morning. These things sound cheesy and right out of a self help book, but I do them both. It's all about creating new pathways in our brains--happy ones!
Another idea is to try to think about things that you are going to do that day. Not like take out the trash and go grocery shopping, but what can you do FOR other people. Maybe your friend's birthday is coming up, think about what kind of cake you can bake them or something nice to write in their card. Maybe try to open doors for as many people as you can that day, or perhaps go out of your way to compliment one of your coworkers. it helps to take the focus off yourself and instead think about others.
One more idea is to keep a book, computer, phone, or crossword by your bed. If you wake up with anxiety, start doing something else to take your mind off things until you feel ready to get out of bed.
I think that morning anxiety comes from our anticipating that its going to be there. Try not to search for your anxiety in the morning. If it's there, it's there, but if you have a brief moment of feeling good, don't go looking for those bad feelings!
I wish you all the best and hope this was at least a little bit helpful.