Bardot says she would carry out the threat if French authorities do not reverse a decision to euthanise two sick elephants at a zoo in Lyon.
“If those in power have the cowardice and insolence to kill the two elephants Baby and Népal…I have decided to ask for Russian nationality in order to flee this country, which is now just an animal cemetery,” she said in a statement posted on the website of her foundation, an animal rights group.
The two elephants face being put down because they have been diagnosed with tuberculosis and deemed a threat to the health of other animals and visitors to the Tete d'Or Zoo in Lyon.
Authorities ordered the elephants be put to sleep last month, prompting an outcry that resulted in them being granted a temporary reprieve over Christmas.
Bardot's announcement came a day after fellow actor Depardieu was granted Russian citizenship in an on-going tax row with the French government.
Reaction to her decision has been swift on social media networks. The hashtag #JeDemandeLaNationalitéRusse (I demand Russian Nationality) has been trending on Twitter.
“I’m not convinced they are less cruel to animals in Russia compared to France,” one tweet said.
“Vladimir Putin gives psychiatric asylum to Depardieu and Bardot,” another wrote.
"Dear McDonald's: give me more mayonnaise and ketchup, or I will demand Russian nationality," another tweet said.