| Week | Date | Rank | Rec | Points | FPV | CP | Last Week |
|---|---|---|---|---|---|---|---|
| 1 | Sep 23 | 18 | 1-0 | 23 | 0 | W 20-14 at LSU | |
| 2 | Sep 30 | NR | 0 | 0 | |||
| 3 | Oct 7 | 15 | 2-0 | 76 | 0 | ||
| 4 | Oct 14 | 19 | 2-1 | 29 | 0 | ||
| 5 | Oct 21 | 13 | 3-1 | 103 | 0 | ||
| 6 | Oct 28 | NR | 0 | 0 | |||
| 8 | Nov 11 | 20 | 4-3 | 26 | 0 | ||
| 9 | Nov 18 | 13 | 5-3 | 146 | 0 | ||
| 10 | Nov 25 | 9 | 6-3 | 384 | 0 | ||
| Final | Dec 2 | 8 | 7-3 | 1186 | 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.