Jagtar Singh Johal, who has been detained for almost five years without trial, appeared in person in court in Delhi today and was formally charged.
He is accused of conspiracy to murder and being part of a terrorist gang.
A separate online letter, which campaigners hope will attract up to 20,000 signatures including 90 per cent of MPs, was to be handed following a protest at 10 Downing Street today.
In his letter, Mr Johal congratulates Ms Truss on her appointment and says he hopes his “freedom will not be traded in return” for increased business links between the UK and India.
He writes: “I hope you show more guts than your predecessors when it comes to addressing the issue of UK citizens languishing in Indian prisons for years without trial.”
He also describes his case as “highly politically motivated” and urges the new prime minister to “make a stand and act” to secure his release.
“Otherwise,” the note continues, “as is evident with cases of Sikh political prisoners and minorities in India, decades can pass waiting for justice.”
The online letter states: “The UK Government under new leadership must now urgently use all its diplomatic efforts to get Jagtar released and re-united with his family in Scotland.”
Mr Johal, 35, from Dumbarton, was arrested in India's northern Punjab region in November 2017 two weeks after his wedding. He is accused by the Indian government of being part of a terrorist plot which carried out the murders of prominent right-wing religious figures in spring 2017.
His family say he has been targeted because of his political activism in documenting the persecution of Sikhs in the Punjab in 1984.
The UK government had previously said it has consistently raised his case with the government of India.
Earlier this year, the UN's Working Group on Arbitrary Detention said Mr Johal should be released immediately.
The panel of experts said his detention was arbitrary, lacked legal basis and was also motivated by his Sikh faith.