The Warriors face Saracens in a quarter-final clash at Vicarage Road a week on Sunday and Rory thinks Sean Lineen's team can go one better than their last visit to Watford.
Rory will move south next season after clinching a two-year deal with Sale Sharks but said in the Record: "I won't be thinking about that until I have got the job done with Glasgow.
"I have had a great season since recovering from groin problems but the next few weeks are a massive chance to put the Warriors and Scotland on the map.
"I don't think Glasgow have had the credit they deserve for their efforts under Sean. We are a good team and are improving steadily.
"Now we have the chance to prove how good we are. I have no doubt at all we can go to London and beat Saracens despite losing there in the group stages.
"We played some brilliant rugby against them in truly wretched conditions. The only reason they beat us was they had more power in the scrum and I know our pack have come a long way since then.
"Guys such as Euan Murray have picked up a load of experience in a short period of time and I am confident they can provide the ideal platform for the backline - plus it should be a much firmer surface which will suit us better. We have the guys who can cut them up."