The body said Ping had been asked by African leaders to appoint a "high-level personality" who could garner support and generate more attention to the conflict in the Horn of Africa nation, which has not had an effective government since 1991.
Rawlings, 63, will be tasked with "mobilising the continent and the rest of the international community to fully assume its responsibilities and contribute more actively to the quest for peace, security and reconciliation in Somalia", it said in a statement.
The appointment of Rawlings, who ruled Ghana for two decades, first as a military leader then as elected president, comes at a time when AU troops are engaged in fierce battles with Islamist rebels bent on toppling the internationally-backed adminstration in Mogadishu.
On Monday, Somali government forces and their AU allies seized control of positions occupied by the insurgents in fighting that left at least 15 people dead.
The AU troops, numbering some 7 200 soldiers, remain the only obstacle between the Shabaab and a total take-over of Mogadishu, where the Western-backed government has been confined to just a few blocks by the near-daily clashes.