I saw posts about this yesterday, and I'd always been curious about this, so I put it together. I may have missed a game or two, but this should be pretty accurate. I started in '96 and I used the AP poll because they have a final poll in January. There was at least one game (Tulsa, last year) where we knocked them out of the poll to end the season, so it doesn't count as a win against a final ranked team, but it would've counted as a loss if we've lost. This is all a bit biased against us since a win against us would increase the chance a team is ranked, while a loss would do the opposite. Anyway, here it is:
Record since 1996: 11-81
Record since 2001: 5-70 (2021 is tbd because we don't have a final poll yet)
1996 - Bama W, LSU L, Auburn L
1997 - LSU L, Georgia L, Auburn W, Ole Miss L
1998 - Arkansas W, Tennessee L, Texas L
1999 - Alabama L, Arkansas L, Ole Miss W
2000 - Florida W, South Carolina L, LSU L, Auburn W
2001 - South Carolina L, Florida L, BYU L, LSU L
2002 - Alabama L, Auburn L
2003 - LSU L, Ole Miss L, Tennessee L
2004 - Auburn L, LSU L
2005 - Auburn L, Georgia L, LSU L, Florida L, Alabama L
2006 - LSU L, Auburn L, Arkansas L, Georgia L, West Virginia L
2007 - LSU L, Tennessee L, Auburn W
2008 - Georgia Tech L, Alabama L, Ole Miss L
2009 - Georgia Tech L, LSU L, Ole Miss W, Alabama L
2010 - Auburn L, Alabama L, LSU L, Arkansas L
2011 - Alabama L, Arkansas L, LSU L, Georgia L, South Carolina L
2012 - Alabama L, Texas A&M L, LSU L
2013 - Oklahoma St L, Auburn L, LSU, L, South Carolina L, Texas A&M L, Alabama L
2014 - Georgia Tech L, Ole Miss L, Alabama L, Auburn W
2015 - Alabama L, LSU L, Ole Miss L
2016 - Alabama L, LSU L, Auburn L
2017 - LSU W, Georgia L, Auburn L, Alabama L
2018 - Iowa L, Texas A&M W, Kentucky L, Florida L, LSU L, Alabama L
2019 - LSU L, Auburn L, Alabama L
2020 - Alabama L, Texas A&M L, Georgia L
Record since 1996: 11-81
Record since 2001: 5-70 (2021 is tbd because we don't have a final poll yet)
1996 - Bama W, LSU L, Auburn L
1997 - LSU L, Georgia L, Auburn W, Ole Miss L
1998 - Arkansas W, Tennessee L, Texas L
1999 - Alabama L, Arkansas L, Ole Miss W
2000 - Florida W, South Carolina L, LSU L, Auburn W
2001 - South Carolina L, Florida L, BYU L, LSU L
2002 - Alabama L, Auburn L
2003 - LSU L, Ole Miss L, Tennessee L
2004 - Auburn L, LSU L
2005 - Auburn L, Georgia L, LSU L, Florida L, Alabama L
2006 - LSU L, Auburn L, Arkansas L, Georgia L, West Virginia L
2007 - LSU L, Tennessee L, Auburn W
2008 - Georgia Tech L, Alabama L, Ole Miss L
2009 - Georgia Tech L, LSU L, Ole Miss W, Alabama L
2010 - Auburn L, Alabama L, LSU L, Arkansas L
2011 - Alabama L, Arkansas L, LSU L, Georgia L, South Carolina L
2012 - Alabama L, Texas A&M L, LSU L
2013 - Oklahoma St L, Auburn L, LSU, L, South Carolina L, Texas A&M L, Alabama L
2014 - Georgia Tech L, Ole Miss L, Alabama L, Auburn W
2015 - Alabama L, LSU L, Ole Miss L
2016 - Alabama L, LSU L, Auburn L
2017 - LSU W, Georgia L, Auburn L, Alabama L
2018 - Iowa L, Texas A&M W, Kentucky L, Florida L, LSU L, Alabama L
2019 - LSU L, Auburn L, Alabama L
2020 - Alabama L, Texas A&M L, Georgia L