Reece Coombs was with his girlfriend in The Albany Palace, Trowbridge, when he felt something on his leg.
After the "sewer rat-sized" rodent climbed his leg, Mr Coombs said the pub was cleared by staff and pest controllers were called in.
JD Wetherspoon confirmed two rats were spotted on the premises but said the issue was now "under control".
Mr Coombs said he had been enjoying a meal with girlfriend Lucy Wrenn on Tuesday when he felt something on his leg.
"It felt like somebody had kicked me, then a rat ran up my leg and took the chip out of my hand and bolted.
"I thought, 'that rat has some serious confidence'.
"I didn't know whether to laugh or cry. I can't stand rats and you never expect that kind of thing in a restaurant."
Mr Coombs said he told staff, who immediately cleared the pub, leaving other customers "confused why they were getting kicked out".
The pub gave the couple a full refund but Mr Coombs said he is "still not happy" about what happened and plans to take the matter further.
A Wetherspoon spokesman said the company "was aware that a rat took a chip which had fallen on the floor from a customer's meal", but could not confirm it had run up Mr Coomb's leg.
The pub was closed for 30 minutes while pest controllers dealt with the rats, he said, and customers were "understanding of the situation".
"We are not sure how the rats came into the pub, however there has been some fly tipping in the alley at the rear of the pub and this might have been a factor," he added.
"We aim to uphold the highest standards in our pubs at all times and apologise to customers for this situation."
A pub customer has claimed a rat ran up his leg and took a chip out of his hand while he was eating.