Tithing is part of the Law, under the Old Covenant. As Christians under the New Covenant, we are not bound by the Law, but by the leading of the Holy Spirit who lives within us. If He leads you to pay your tithe to a motherless babies home, then be blessed in doing so.
If it's a sin to help out the orphans, I'm going to have to cross out a few passages of Scripture. But I'm guessing you're asking if it is okay to use the money you would normally tithe to your local church to send to the orphanage, in which case I concur with Revlynn.