The Hannah Park outfit will travel to Ayrshire in a battle of the Super Premier basement with both clubs rooted to the foot of the table.
Fellow Lanarkshire side Rutherglen Glencairn will host the visit of Camelon, Linlithgow Rose will play Bo'ness United, and Kelty Hearts will battle it out with Auchinleck.
All ties will take place at 2.30pm on Saturday, March 16.
Linlithgow Rose v Bo'ness United
Rutherglen Glencairn v Camelon Juniors
Cumnock v Shotts Bon Accord
Kelty Hearts v Auchinleck Talbot