Can an arranger claim copyright for a previous written song?

There are many issues to consider. First, if you have not registered copyright, go quickly and do that at Copyright dot gov. Do not do this anywhere else. That address is the U.S. Copyright office and it will cost you $35 to register copyright. Second, making a new arrangement is creating a derivative work. As the owner of the copyright on the original song, you have the right to control who makes a derivative work. If you agreed to let the man make a new arrangement, then he should be able to register copyright as the arranger on his new work, with you as the person who created the music, which is the melody, and the lyrics. So, yes, you will be co-owners on the copyright on the new arrangement. If you wanted the man to create a new arrangement for a flat fee, as a work for hire, you would have had to have a contract in writing in advance, before he did the work, that clearly stated it was a work for hire and that you would own the copyright and he would not and that he was giving up certain rights and ownership. If you did not have such a contract in advance of him doing the work, then it is too late, because the law requires such agreements for works for hire to be made in advance. Since the man is part owner of the copyright on the new arrangement, he can register copyright on his arrangement. He can also collect a share of the songwriter royalties, if any should occur. It sounds like you two now need a good contract that spells all this out. Please have the contract written by a lawyer who actually knows music law. You asked if the man could ever win in court. Yes, he sure could. But you two should not be thinking of suing each other. You should be thinking about sharing ownership of the wonderful song you two have created and of how you are going to promote the song. Lawsuits are for people who cannot cooperate and create nicely with others. Let's hope you two are not like that.