The answer to your question is, "onto", but the correct way would be just "on" or "to" depending on where the tree is located.
If the tree is standing up, then there is nothing for her to be on top of, so you do not need "on", just "to". "She is tied to the tree with rope." If the tree is laying on the ground and she is on top of the tree, you do not need "to", just "on". "She is tied on the tree with rope."
If you want to use "on to" it would be something like, "She got on to save a cat."