You probably know all this (cut and paste from an archived version of the now defunct regiments.org ......) Since I gather that the various Companies of the RCRR were spread out along the U.S border, it sounds like you might have to know which Company he was in, and then proceed from there ....
1840 - The Royal Canadian Veterans Regiment raised as a British Army regiment with HQ at Toronto, from volunteers of good character with a proven record of good conduct in the score or so British regiments then serving in Canada. Canadian pensioners who had served 15 years in a British regiment were also eligible for service. The term of service was ten years, after which men could purchase land at a discount, and be eligible for service in the Canadian Militia. The regiment's purpose was to deter deserters from British line regiments to the economically-attractive United States, as well as to provide the first line of defence against attacks from the U.S. The normal establishment was ten companies scattered along the American frontier, but it actually fluctuated over time between six and fourteen.
1840 - The Royal Canadian Regiment [not to be confused with 1883 Royal Canadian Regiment]
1840 - The Royal Canadian Rifle Regiment
1855 - HQ moved to Kingston
1862.12.02 - absorbed Royal Newfoundland Companies (two coys which continued to garrison Newfoundland)
1870.09.30 - disbanded in Canada; some personnel transferred to 1st Bn, 60th King's Royal Rifle Corps; 543 members settled in Canada (including 262 who joined the Canadian Militia)The link below goes to a page at Global Genealogy with some information, which includes the fact that records are held by the Public Records Office in the UK, with a list of specific microfilm references. The other good news is that copies of these microfilms are also held by the Family History Library of the LDS (Mormon) church in Salt Lake City .... and that some LDS Family History Centers (there is one in every LDS "stake" I believe) have these microfilms, or can order in copies. (I know from experience that they are more than willing to let people who are not LDS members use these facilities.)
http://globalgenealogy.com/globalgazette/canada-military/british-in-cda/roal-cdn-rifles-1840.htm