His party colleague, Union minister Smriti Iran, also took oath as member of the Upper House.
While Shah took his pledge in Hindi, Irani took hers in Sanskrit.
Both the leaders, accompanied by their spouses, were administered the oath in Rajya Sabha Chairman M Venkaiah Naidu's chamber.
The two leaders, who were elected to the Rajya Sabha from Gujarat earlier this month, were accompanied by Parliamentary Affairs Minister Ananth Kumar, Finance Minister Arun Jaitley, External Affairs Minister Sushma Swaraj, Food Minister Ram Vilas Paswan and Law Minister Ravi Shankar Prasad among others.
After the oath, he and his wife called on BJP veteran leader L K Advani at his residence to seek his blessings, party leaders said.