An African writer can be a social critic to the extent that any writer can be a critic of the time and place he lives in. But it seems like you are asking for some examples of African Writers who have written about their social circumstances.

Mark Mathabane wrote "Kaffir Boy" and several other autobiographical books about the life of a young black boy growing up in the system of Apartheid in South Africa. In addition, he, through the eyes of his sister, has given the female perspective of life under Apartheid. Therefore he analyses and criticizes the system of apartheid.

Chinua Achebe wrote "Things Fall Apart" which can be read as a novel about the effects of colonization on Igbo society. Through the events which happen, the author shows the disadvantages that colonialism had on the Igbo society.

A current influential book is "Child Soldier Fighting for my Life" by the female Ugandian writer, China Keitetsi. This book is about the story of her life as a child soldier. Keitetsi is an outspoken activist about his topic.

Wikipedia has a few pages about African writers and their books with plot summaries. This might be a good place to start. Below are two additional cites which focus on African writers.