Making good quality Scrabble tiles from scratch was perhaps a little too ambitious, but making labels to stick to existing Scrabble tiles was definitely an option.
This instructable uses an inkjet printer to print the stickers, and a Cricut paper cutter to cut them to exactly the right size to stick to the Scrabble tiles. You'll also need a rotary guillotine (or a metal edge at least a foot long plus a sharp cutting knife - either a scalpel or an exacto knife)
By the way I'm using the old-style plastic tiles that came before the wooden ones in the USA. These are still the current design in Europe and Mexico. (You can find them on eBay fairly often; I bought mine in Mexico which is just a few miles away from where I live)
(This technique should be possible with the wooden tiles but the artwork will have to be created differently to match.)