The Quinnipiac University poll out Thursday shows the Democrat's job approval rating at a five-year low of 36 percent, compared with 41 percent who disapprove of his performance.
It also shows 44 percent think Menendez isn't honest and trustworthy, compared with 28 percent who believe he has those qualities.
Menendez was recently named chairman of the Senate's Foreign Relations Committee. But his ties to a Florida eye doctor and political donor have been referred to a Senate ethics panel.
Menendez reimbursed the doctor $58,000 for flights to the Dominican Republican aboard his private plane.
The poll of 1,1,49 registered voters was taken Feb. 13-17 and has an error margin of plus or minus 2.9 percentage points.