After gluing the the two pieces of wood in position with wood glue and holding the joint until it's reasonable stable, drill two pilot holes through the joint so the wood doesn't split. The holes must be the same size as the dry-wall screws.
secure screws into wood block
Drive the Screws Into the Holes
Insert the screwdriver shank into the holes, making sure that it will pass without binding. Drive the dry-wall screws into the pilot holes, countersinking the heads in the wood base. Clean up any excess glue. Fill screwhead holes with wood filler.