Mnangagwa's Twitter account was only verified on Friday: by late Sunday afternoon it already had 33 000 followers.
The new president, who took over from his boss Mugabe after the military stepped in last November, used one of his first tweets to urge Zimbabweans not to be violent in next year's polls.
'No fighting, no conflict'
Tweeted Mnangagwa: "When we go to the elections you should not fight. When people support their parties it's their choice. We should work for the people and not be selfish. There should be justice and national reconciliation because we cannot progress when communities are in conflict." The tweet has had more than a thousand likes.
Though Mnangagwa is a member of the same party as Mugabe, there are huge hopes - which some believe are misplaced - that he will turn the page on Zimbabwe's past 17 years of bitter political fighting and bring back the economic stability the country desperately needs.
Courting the youth vote
There were some fairly muted complaints about the quality of Mnangagwa's first social media video - which shows him sitting in a homely environment to address the nation. But on the whole it's been well received.
Wrote Tee G Cee on FB: "They should have taken off those cloths on your sofas. They are outdated now."
Mnangagwa knows this year's poll will be contested most tightly at youth level. With cellphone penetration at just about 100% in Zimbabwe, his campaign has just started with a bang.