Wendron are the last Combination League side left in the competition after St Day were beaten 6-3 by St Austell at Poltair Park.
Last season's winners Bodmin are aiming to complete yet another league and cup double.
Wendron boss Paul Murray says the odds are against his side, but the 'dron are determined to "enjoy it and give a good account of ourselves."
Elsewhere Falmouth Town face Eluburton Villa in the Peninsula League premier division. In division one west Penryn host Vospers Oak Villa, and Porthleven welcome Holsworthy to Gala Parc.
Meanwhile Helston Athletic face Perranporth at Kellaway Park in the quarter final of the Cornwall Charity Cup.
RUGBY: Falmouth Eagles play table-topping Exeter University at the Recreation Ground, and Penryn travel to promotion-chasing Ivybridge.