Swati Vadlamudi's cartoon depicts a conversation between Hindu god Ram and his wife, Sita, to criticise right-wing support for the accused.
In the cartoon, Sita tells Ram she is "glad" she was kidnapped by demon king Ravan and not her husband's followers.
Ms Vadlamudi said the threats have only made her "stronger".
The illustration has been shared by thousands on social media, but her use of the characters from the Hindu epic Ramayana in the cartoon has sparked controversy.
Ms Vadlamudi told BBC Telugu's Prithvi Raj that drawing satirical cartoons was a hobby of hers.
She said the illustration was meant to condemn two gruesome incidents of rape which made national headlines last week.
An eight-year-old Muslim girl from Kathua district in Indian-administered Kashmir was brutally gang raped and murdered - outrage grew after two ministers from the Hindu nationalist Bharatiya Janata Party (BJP) attended a rally in support of the accused men, who are Hindu.
In another case, a 16-year-old girl attempted suicide outside a BJP lawmaker's house after alleging that he raped her.
In an interview with BBC Telugu, Ms Vadlamudi said both incidents "involved India's ruling BJP - either leaders who have committed a crime or supporters who have backed the offenders".
She said that many of those who defended the accused or insisted on their innocence identified themselves as "bhakts" or "zealous devotees" of the god Ram.
Given the brutality of these crimes, she said she couldn't help but wonder what would have happened to Sita if, in the epic, she had been kidnapped by these so-called "Ram bhakts".
After the cartoon was published, she has received numerous threats online, with many calling for her arrest.
Some of the threats also referred to the recent murder of an Indian journalist who was known for casting a critical eye on Hindu fundamentalism.
"I can't sleep at night because of the threats on social media," she said, adding that her family was concerned over her safety.
Indian police have registered a case against Ms Vadlamudi after a right-wing group insisted the cartoon hurt the religious sentiments of Hindus. Women's groups and the Indian Journalists Union (IJU) have condemned the complaint against her, calling it an "attack on the press".
In the last few years, journalists seen to be critical of Hindu nationalists have been berated on social media, while many women reporters have been threatened with rape and assault.
The Committee to Protect Journalists, a non-governmental organisation, has ranked India as a country with a poor record in safeguarding journalists.
Their research shows that at least 27 journalists have been murdered because of their work in India since 1992.
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