In his letter, Mr Sinha said any hesitation on his part to appear before the JPC will prove that he has "something to hide".
Mr Sinha pointed out that when Parliament's Public Accounts Committee (PAC) was examining the Comptroller and Auditor General (CAG) report on the 2G scam, the Prime Minister had publicly offered to appear before it to enable the committee to reach the "right conclusions".
"You have not made a similar offer to the JPC despite the fact that many members of the JPC have publicly demanded that you appear before the JPC," Mr Sinha said.
He claimed that in his communications to the JPC, Mr Raja has levelled "serious allegations" against the Prime Minister and Finance Minister P Chidambaram.
"I think it is in your own personal interest to appear before the JPC and clear your name. You may also suggest the Finance Minister to make a similar offer," he wrote.
Mr Sinha asked the Prime Minister to request JPC Chairman PC Chacko to call Mr Raja as a witness before the committee.
"Any hesitation on your part will only confirm the feeling that you have something to hide," the BJP leader said.
In a separate letter to Lok Sabha Speaker Meira Kumar, Mr Sinha recalled Mr Raja's request to her to be called before the JPC as a witness.
He said despite several letters, Mr Chacko has not entertained the request.
"If you also remain indifferent to the goings on, then Parliament of India will undoubtedly suffer a great setback," he said.
Earlier in the day, Mr Sinha hit out at Mr Chacko for not calling Mr Raja as a witness and alleged that the panel could be used to "conceal the truth" in the 2G scam rather than expose it.
He also dubbed the decision of not calling Mr Raja as a "serious omission."
The BJP and Left members in the Committee have been backing Mr Raja's plea that he be allowed to depose before the panel.