Not in 1963. Outboard titles did not start until 1994 I believe. If you were not the owner in 1994, someone before you could have titled it already. There is a serial number search tool on the TPWD website. You can check any outboard's status there. In your case, a "not found" would mean it has never been titled.
The state may require that you title it before you sell it (if you follow their rules). It looks like there are a couple of forms to accomplish that task.