The Scottish champions were knocked out in the third round by Morton, making it a very even affair from the quarter-final stages, as Rankin and the Terrors prepare for their trip to Inverness.
"At this stage, and after seeing the result on Tuesday night with Morton putting Celtic out, I think everybody fancies their chances now,” he said.
"On a one-off day, you fancy your chances against Celtic.
"But, when you see that they're not in the competition, all players are now thinking 'our name's on this trophy'.
"We are no different from any other club. We fancy our chances. It's there for anybody to take and hopefully it can be us."