Not a jig, I am afraid, but there is Staines Morris

Come ye young men, come along
With your music, dance and song
Bring your lasses in your hands
For tis that which love commands

   Then to the Maypole haste away
   For 'tis now our holiday

Or how about the Rocky Road to Dublin, which mentions jigs!:

From there I got away, My spirits never failin'
Landed on the quay As the ship was sailin';
Captain at me roared, Said that no room had he,
When I jumped aboard, A cabin found for Paddy,
Down among the pigs I played some funny rigs,
Danced some hearty jigs, The water round me bubblin',
When off Holyhead, I wished myself was dead,
Or better far instead, On the rocky road to Dublin.

Not actually a TRAD song, but old.

Or
Up to the Rigs:

Up London City I took my way
It was up Cheapside I chanced to stray
When a fair pretty girl there I did meet
And with kisses her then I did greet

cho: For I was up to the rigs,
Down to the jigs
Up to the rigs of London Town

Not sure if these jigs are dances, though.

The Bodleian Ballad library contains a number of songs, such as
The Donnybrook jig