Not with complete certainty, as staff cars were a routine target of opportunity and several were attacked on July 17th. A 1944 Reuters report credited Typhoons of 193 Squadron, but post-war it was found that they were operating in the wrong area. Volume III of the official RAF history says "It is now known that the squadron concerned was No. 602, whose Spitfires, according to German eye-witnesses, dived on Rommel's car that evening when it was near the appropriately named hamlet of Ste. Foy de Montgomerie." Shores & Thomas' 2nd Tactical Air Force has a section, "Who Got Rommel?", that notes disparities between the time and location of 602 Squadron sorties and witness accounts of the attack on Rommel; it concludes "... it could have been 602 Squadron that took Rommel out of the battle but, on today's available evidence, the 'proof' hardly seems conclusive."
For some reason the otherwise comprehensive Shores & Thomas don't mention 412 (RCAF) Squadron, who on current evidence appear to have the strongest claim. Reginald Byron, archivist at the Tangmere Military Aviation Museum, has put together a page "Who Shot Rommel?" with extensive documentation showing Charley Fox and Ed Prizer of 412 Squadron attacked a staff car at the right place and time, concluding "Although we can never be absolutely certain, the circumstances fit together nicely, strongly suggesting that either Fox, or Fox and Prizer together, hit Rommel’s car."