The Constitution has not fixed the term of office of members of the Rajya Sabha and left it to the Parliament. Accordingly, the Parliament in the Representation of the People Act (1951) provided that the term of office of a member of the Rajya Sabha shall be six years. 

The Act also empowered the President of India to curtail the term of members chosen in the first Rajya Sabha. In the first batch, it was decided by lottery as to who should retire. Further, the Act also authorised the President to make provisions to govern the order of retirement of the members of the Rajya Sabha. Under this, the president has made the Rajya Sabha (Term of Office of Members) Order, 1952. 

The term of the Rajya Sabha is six years, but a member elected in a bye-election serves for the remainder of the term of the vacancy caused.

Further Reading:

• Rajya Sabha
• Lok Sabha 
• Election of Government: Methods