From what my research can determine, tOSU has played an opponent ranked #1 in the AP football poll 12 times.
The Buckeyes record in those 12 games is 3-3 in Columbus, 1-1 in Bowl Games, and 0-4 on the road.
Wins against AP #1 (N/R = Not Ranked)
10-11-1952..N/R tOSU 23, #1 Wisconsin 14...Columbus
10-12-1968..#04 tOSU 13, #1 Purdue 0........Columbus...NC year for tOSU
11-02-1985..#08 tOSU 22, #1 Iowa 13.........Columbus
01-03-2003..#02 tOSU 31, #1 Miami 24 (2OT).Tempe......NC year for tOSU
Losses against #1 (N/R = Not Ranked)
10-26-1940..N/R tOSU 07, #1 Cornell 21.......Ithaca, NY
11-22-1947..N/R tOSU 00, #1 Michigan 21....Ann Arbor
11-20-1948..#18 tOSU 03, #1 Michigan 13....Columbus...NC year for TSUN
10-06-1951..#07 tOSU 20, #1 Mich. St. 24...Columbus
10-15-1966..N/R tOSU 08, #1 Mich. St. 11....Columbus
01-01-1973..#03 tOSU 17, #1 USC 42..........Pasadena...NC year for USC
10-29-1994..#21 tOSU 14, #1 Penn St. 63....State College
11-22-1997..#04 tOSU 14, #1 Michigan 20....Ann Arbor...NC year for TSUN
Wins when tOSU was AP #1 and opponent was AP #2
01-01-1969..#1 tOSU 27, #2 USC 16............Pasadena...NC year for tOSU
09-09-2006..#1 tOSU 24, #2 Texas 7...........Austin
Combined with the games vs #1, this means that tOSU is 6-8 all-time when playing their highest-ranked possible opponent.
In response to Dubs' question, there are these games (NOTE - the list of road wins over #2 opponents may not be complete, but 1983 Oklahoma was a road win against an AP #2 team).
Non-home wins against AP #1 or AP #2 ranked teams
09-17-1983...#6 tOSU 24, #2 Oklahoma 14...Norman
01-01-1969...#1 tOSU 27, #2 USC 16..........Pasadena...NC year for tOSU
01-03-2003...#2 tOSU 31, #1 Miami 24 (2OT).Tempe.....NC year for tOSU
09-09-2006...#1 tOSU 24, #2 Texas 7.........Austin