| Week | Date | Rank | Rec | Points | FPV | CP | CFP | Last Week |
|---|---|---|---|---|---|---|---|---|
| Pre | Aug 12 | 21 | 0-0 | 237 | 0 | 21 | -- | DNP |
| 1 | Sep 3 | 20 | 1-0 | 339 | 0 | 18 | -- | W 61-39 vs New Mexico |
| 2 | Sep 8 | 20 | 2-0 | 381 | 0 | 18 | -- | W 22-10 vs Northern Arizona |
| 3 | Sep 15 | RV | 15 | 0 | RV | -- | L 31-7 at #14 Kansas State | |
| 4 | Sep 22 | RV | 2 | 0 | RV | -- | DNP | |
| 5 | Sep 29 | RV | 106 | 0 | RV | -- | W 23-10 at #10 Utah | |
| 6 | Oct 6 | NR | 0 | 0 | RV | -- | L 28-22 vs Texas Tech |
Note: Arizona's ranking in the final 1961 poll has been changed to unranked after the original AP wire story and poll was revisited and confirmed across several newspapers.