[1] Rajbanshi was the Indian National Congress candidate for Balipara in the 1972 Assam Legislative Assembly election.
Rajbanshi was the Indian National Congress candidate for the newly established constituency of Rangapara in the 1978 Assam Legislative Assembly election.
He was later inducted into the Kesab Chandra Gogoi cabinet as minister for electricity, mines, parliamentary affairs and animal husbandry.
[8][10] In the 1985 Assam Legislative Assembly election, Rajbanshi sought reelection as the Indian National Congress candidate for Rangapara.
Moving the debate Rajbanshi stated that Assamese youths were joining the ULFA because AGP had failed to fulfil the aspirations of the people.
[11] Chief Minister Prafulla Kumar Mahanta said that Congress had no right to criticise his government as they too had committed many misdeeds while in power.
He said that his government held all-party meetings to combat extremism in Assam and sought the views of all political parties in this regard.
[6] He did not seek reelection in Rangapara after serving as MLA for 18 years, and he was succeeded by the Congress candidate Bhimananda Tanti.