It was revealed earlier this week that the former taoiseach will front an Irish-language television series on RTÉ about old railway routes.
As a fluent Irish speaker, the ex-Fine Gael leader will present the show in his native tongue.
It is understood the show, being produced by Feiristeach Sonas Productions, will air late next year.
However, members of the public have taken to Twitter to vent their frustration that a former politician nabbed the role, as opposed to another Irish speaker who has experience in presenting or someone who already works in the arts.
A petition has been created online calling for the show to be cancelled, or for the Mayo man to be replaced as the host.
The petition reads: ‘It’s completely inappropriate for the State broadcaster to give a vanity series like this to a former taoiseach and to promote the Fine Gael party who are in government.’
As of last night, almost 600 people had signed the petition.
A spokeswoman for RTÉ told the Irish Daily Mail that no official complaints have been made to the broadcaster in relation to Mr Kenny’s new role.