Mr. Moore, a former judge, leads Democrat Doug Jones, a former federal prosecutor, 49 percent to 43 percent among likely voters, according to the poll.
The Washington Post published a bombshell report last month on the allegations based on interviews with more than 30 people.
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The CBS poll said half of Moore's supporters are backing him because they want a senator who would cast votes for conservative causes, rather than because they think he is the best candidate in the election.
Nine women reportedly have made allegations against Moore.
Moore has said that he never met Corfman, and denies numerous allegations against him.
Meanwhile, a CBS News/You Gov poll shows that 71 percent of Alabama Republicans believe the allegations against Moore are false, and almost all those believe that Democrats and the media concocted the allegations.
The margin of error is 4.5%.
Three late-November polls, however, show Moore leading Jones.
At the time, he joined a growing number of lawmakers who were calling for Moore to step aside in the race. And an Emerson College poll released Tuesday showed 53 percent of likely Alabama voters supported Moore. Just 35 percent of likely voters said they believe Moore pursued relationships with teenage girls when he was in his 30s, while 37 percent said they are either unsure or do not have an opinion, and 28 percent said they do not believe the allegations, the poll found.
Abortion is among the top issues pulling voters toward Moore. Seventeen percent believed the allegations to be true. And across all Alabama voters, 47 percent said they trust Moore on the issue while 46 percent said they trusted Jones.
Nationally, Republicans have largely pulled their support for Moore.
Other key Republicans have called for Moore to drop out of the race, including Senate Majority Leader Mitch McConnell and House Speaker Paul Ryan and two former Republican presidential nominees, Mitt Romney and Senator John McCain.