Trade union Unite said the "vicious cost-cutting measure" was a "kick in the teeth" for the workforce at the taxpayer-backed bank, which has already cut 30,000 jobs since 2008.
The latest job losses will affect the support unit in Brighton and Unite said those in line to lose their jobs are long-serving staff with years of experience.
Unite national officer Rob MacGregor said: "We were told when the losses were announced in February that the bank would be slimmed down to be more UK-focused and that it would place greater emphasis on the UK consumer.
"But here we are five months later and the bank is taking jobs out of the UK and sending them to India. There are indications that this maybe the start of a programme of continued offshoring.
"This decision by RBS is a clear kick in the teeth to the loyal and experienced workforce in Brighton, as well as an assault on UK taxpayers who bailed out the bank."
RBS, which is 82 per cent owned by the UK taxpayer, received a £46 billion government bailout in the wake of the 2008 financial crisis.
It has warned that further cuts may follow as part of a restructuring programme introduced after the bank posted full-year losses of £8.2 billion.
However, a spokeswoman said there were no plans at the moment to outsource further jobs.
She added: "This is clearly difficult news for staff affected by these changes and we will do everything we can to support them through this time. These changes are part of the cost-cutting we are undertaking to make this a simpler bank for customers."