Play in the key of D or G, and do it in 6/8 time.
A "jig" is a type of folk music normally played in compound meter, and the jig most often associated with Irish music is 6/8, sometimes 12/8. So at the very least, try strumming a G chord and hopefully you have enough wits about you to count to 6 when you do it. Check out the video below for help with the dynamics.
If you're feeling frisky, you can try a "slip jig," which is a jig performed in 9/8 time. But honestly, I feel orchestrating a slip jig in 9/8 at a high tempo after 8 pints of Guinness is asking a little much.
Now let's assume one of your hands has gone completely numb at this point. You can still carry on the tradition of Irish music by tuning your guitar to DADGAD and just using your good hand to strum the open strings. DADGAD is a prevalent tuning in traditional Irish folk and can sound great with very rudimentary chord fingerings. (Again, watch for the video to learn a few.)