The YouGov survey put support for a Yes vote at 33%, trailing backing for No on 52%.
A further 12% were undecided with the rest saying they would not vote in the referendum on September 18.
Support for Yes and No was unchanged from December, though the number of don't-knows fell by a single percentage point.
Looking further back, support for independence was one percentage point higher than in September, according to YouGov's series of polls, while backing for No was the same on 52%.
Nearly 1200 voters were quizzed from January 21-27.