Sinha was in judicial remand from June 3 in connection with an alleged assault of a government official in Hazaribagh the previous day.
After meeting Sinha in jail, Advani had told reporters on Tuesday that Sinha should leave jail after securing bail and lead the ongoing agitation by BJP against the power crisis in Jharkhand.
Sinha was also the 'right person' to be chief minister after the Assembly elections later this year, he had said.
Sinha and several of his supporters were arrested on June 2 after JSEB General Manager (Hazaribagh Branch) Dhanesh Jha filed an FIR accusing them of tying him up during their demonstration near his office.
The following day the court remanded them to judicial custody for 14 days after all the accused refused to seek bail.
The court extended their remand till June 28 after they stayed away from moving bail again on June 16.
On June 12, BJP leaders Shahnawaz Hussain and Rajiv Pratap Rudy as emissaries of BJP president Rajnath Singh had urged Sinha to obtain bail and participate in the party's statewide agitation.
Besides Sinha, all his supporters were also granted bail by the court on Wednesday.