olan, can you explain what you think a letter of acceptance is?
The possible English meanings don't seem to fit what you are asking for.
For example, if you apply to enter graduate school and you are accepted, you may receive a letter of acceptance. That is not something you can just ask for -- you must go through the process, apply, and then wait.
You are perhaps talking about a letter of recommendation, where a professor describes your skills to a university or potential employer, or for a scholarship as you mention. That is almost always given by someone who knows you well.
Perhaps this professor is especially well known, and you are looking for his endorsement to get the attention of the scholarship committee, make it more likely that you'll get the scholarship?
We really need to narrow down what you are going for before we can advise you.
It sounds most likely that you are asking for a letter of recommendation from a professor you do not know well. Lash's advice is good there, with a little tweaking. Something like:
Dear Professor ___________,
I have greatly enjoyed our correspondence and have learned a great deal from it. Thank you.
I will soon be applying for the [name of the scholarship] and would be deeply honored if you could write a letter of support. [You really need to nail down the terminology.]
Then follow the format Lash suggests, basically just try to convince this person that a) you deserve the scholarship, b) his endorsement will help you get it. Flattery is good for the latter.
You can post drafts if you'd like.
But first, get the terminology down. Who told you it was called a "letter of acceptance"?