The role has been advertised after an internal review of the election campaign by former cabinet minister Eric Pickles concluded that the Conservatives should "urgently upscale" their media and digital department as they had been "outfought" by Labour on social media.
Analysis showed that the campaign saw a massive surge in Facebook and Twitter followers for Labour, with Jeremy Corbyn's posts receiving 2.8 million shares compared to just 130,000 for Theresa May.
The Tories’ lack of appeal on social media was underlined when the party’s efforts to go "behind the scenes" using Instagram at its Manchester conference were widely mocked on Twitter.
Recent attempts to emulate Labour's grassroots movement Momentum group fell flat, with the party distancing itself from Activate after a group of alleged supporters were accused of calling for the "gassing of chavs" in a leaked WhatsApp discussion.
And a series of embarrassing memes led to claims that the social media accounts of the Tory-supporting group had been hacked with confusion over whether it was a "spoof" organisation.
The job advertisement stated that candidates should have a "substantive and demonstrable track record and experience of online advertising and marketing, excellent political judgement" and "a commitment to the values of the Conservative Party."
Labour Assembly Against Austerity spokesman Matt Wilgress told the Star: "The reason the Tories’ social media doesn't resonate is because they have policies for the few, not the many.
"Just like their embarrassing attempts to replicate the success of Momentum with the cringeworthy Activate campaign, this is bound to fail."
Meanwhile, Mr Corbyn has given his backing to British indie band Wolf Alice in their bid to top the album charts this week.
He said he was returning the favour after the band, who played at a People's Assembly "Tories Out" national demonstration in June, supported Labour's general election campaign.
In a tweet, the Labour leader said:" "After helping Labour beat the odds in the election, it's great to see @WolfAliceMusic doing the same in the charts."