Singh, 80, submitted his papers before the Legislative Assembly Secretary G P Das in the Assembly premises.
The Prime Minister's Upper House term expires on June 14 and polls for two Rajya Sabha seats from Assam will be held on May 30.
The notification for the elections was issued on Monday and the last date of filing nominations was May 20.
Prior to filing his nomination, he presided over a meeting of Congress Legislature Party in the Assembly.
Singh was accompanied by Chief Minister Tarun Gogoi, Assam Pradesh Congress President Bhubaneswar Kalita and ministers Pradyut Bordoloi, Rakibul Hussain, Neelmani Sen Deka and Himanta Biswa Sarma.
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