How to protect exterior phone line connection from the elements
Yeah, that's a bad joke, I wonder who your phone company is...

If you insist on DIY... it does not particularly need to be waterproof - the splice connectors are filled with grease, so they are waterproof.  Buy a plastic electrical box (no holes) and cut slots in the box part so you can get the cable in place without cutting it. 



Don't make the slots too large. If you want to try for waterproof, use duct seal (gray electrical putty, non-hardening) around the cables in the slot. Screw the cover on, pack some more duct seal on from the outside.

If you choose to use self-fusing tape, choose from the electrical aisle (well, it may not be in your average hardware store/home center, so you might need an actual electrical supply store to find it), not late night TV or plumbing repair. The box is going to be more robust and easier to access.