The answer would be "No He probably can't". We can't answer this from Show canon because show has never mentioned an encounter between Wargs and Dragons. So we have to see the history in books.
Examples of Wargs encountering dragons
Only example of when wargs came face to face with dragons is when King Jaehaerys I Targaryen and his consort Queen Alysanne the Good1 flew north to help the Night's Watch and defeated a host of wildlings, wargs and giants at wall. Pictured Queen Alysanne on Silverwing at the Wall, during the campaign2:
No warg managed to control Vermithor (Mount of Jaehaerys) or Silverwing (mount of Alysanne). This is implied because if a warg had managed that, it would have been a huge event and must have been reported in chronicles of watch or some other record.
This would have also probably caused death of the dragon rider targeted by the warg since the logical move on part of the warg would be to make the dragon throw his/her rider off to the ground. But since nothing like this is reported, we can assume it never happened.
If trained and experienced wildling Wargs could not control dragons, we can assume untrained and green Bran can't either.
Claiming/Controlling a dragon
Still We do not know if skin changers can slip into dragons. Some may say Dragonlords of Valyria might have used some different sort of skin-changing for riding dragons because after a dragon was claimed by a rider, they both shared a bond and became aware of each other (e.g. Dreamfyre broke her chains when her rider Queen Helaena Targaryen jumped from Red Keep to die). But that would be a weak argument. Bond with a dragon seems to be way different.
But anyhow, we know it for Blood-magic, which allowed Dragonlords to claim dragons. Everything the Valyrians accomplished is attributed to their knowledge of blood magic.
Dragons are not like horses, to be ridden by any man who desires. They only serve the person who is their rider e.g. Prince Joffrey Velaryon was thrown to his death by Syrax who was his mother Rhaenyra Targaryen's mount. Aegon the Conqueror flew Balerion but he never dared to mount dragons of his sisters; Vhagar and Meraxes. No Dragon rider has ever claimed two dragons.
All three of Daenerys's dragons were unclaimed previously. Daenerys has now claimed Drogon so he is unlikely to allow another rider until Daenerys lives. Rhaegel and Viserion are however up for taking.
If Bran was trained and knew how to slip into a dragon, we don't know what would have happened. Historically, only people with Valyrian blood have ridden a dragon. But anyhow, Bran does not share a bond with the dragons unlike his wolf (Daenerys did, her dragons could feel her rage & her being in danger and act accordingly). So it is unlikely he could control a dragon. But since as the new Green-seer, Bran would have more powers than most Wargs, we do not know for sure if he can or cannot control a dragon.
1. The tower in which Jojen and Bran were hiding was actually named in memory of Queen Alysanne
2. Art by Emile Denis