Tap into an Electrical Wire Under a Raised Cottage

Several issues at play here:

• First off, everything will depend on the type of wire you are talking about. If it is UF (Underground Feeder) cable, it might be perfectly legal. If it is indoor rated NM (Non-Metallic) cable, a.k.a. "Romex", it is already not to code, so any connection you decide on will not bring it up to code anyway. To be "proper" in that case means redoing the entire run.
• "Splice" by the way implies it has been cut in two and you want to re-join the cut ends. Did you mean you want to TAP into it and have 3 wires now?
• Assuming it is stapled to the joist the chances that you have enough slack to be able to cut into it and add a tap line are slim, because you need extra wire to make the connections with anything like "wire nuts". What you could do (if you have the right tools) is to put "ring-tongue crimp lugs" on the ends of each wire then use screws, nuts and lock washers to attach the rings together, then tape over them with a layer of varnished cambric tape, then electrical tape over that.
• All of this should be done in a weather tight electrical box with a gasketed cover. The thing is, the threaded holes into and out of that box where the cables need to pass through would also need to be sealed. Here's where the type of wire makes a difference. If it is UF cable, they make "UF Cable Seals" (search that term) that you can buy at supply houses. They are a fitting that will thread into the box openings, then the cable is run through a rubber grommet that is then squeezed down to seal around the cable to make a watertight seal. But nobody makes a seal fitting to fit around NM, because, again, this is not something that would be done legally, so they don't make parts to do it. If you want to rig up something non-code compliant anyway, you could try using the UF cable seals anyway, then to make sure, seal around the wires with silicone sealer.