| Week | Date | Rank | Rec | Points | FPV | Last Week |
|---|---|---|---|---|---|---|
| 1 | Oct 6 | 16 | 1-1-1 | 52 | 0 | |
| 2 | Oct 13 | 15 | 1-1-1 | 66 | 0 | |
| 3 | Oct 20 | NR | 0 | 0 | ||
| 7 | Nov 17 | 20 | 4-3-1 | 32 | 0 | |
| 8 | Nov 24 | 18 | 5-3-1 | 17 | 0 | |
| 9 | Dec 1 | 17 | 6-3-1 | 11 | 0 | W 34-6 vs Baylor |
| Final | Dec 8 | 18 | 6-3-1 | 21 | 0 |
Note: Rice'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.