The organisation surveyed 20 countries from the Ivory Coast to Mozambique using Jana, a mobile phone crowdsourcing company.
In return for answering five multiple-choice and two open-ended questions, people received a small payment of mobile airtime.
This is not the first time CNN has partnered with Jana. In March it ran a similar survey to crowdsource opinion from Africans as to whether the continent was ready for an African pope.
At the time Nathan Eagle, the chief executive of Jana, told Journalism.co.uk that most users have "low end feature phones" rather than smartphones or desktop computers.
Many of these phones have a simple web browser, allowing people to click a link in the SMS to see a text-only web page and complete a survey.
The recent survey found that two thirds of Africans are more optimistic now than when Mandela took office, and one in four people says leaders are living up to Mandela’s vision “well”.
However, the results revealed concerns that corruption remains the biggest challenge for African nations.
Peter Bale, vice president and general manager digital of CNN International said: "With the explosive growth of mobile in Africa, mass surveys of this sort are an increasingly interesting way to sample opinions.
"Using a service like Jana to take this survey also allows a brand like CNN to experiment in the world of micro-payments and the sharing economy in Africa where mobile airtime has become a form of currency, particularly among the poor and remote," he added.