A brief excerpt:
This common evangelistic method, known as the altar call or the public invitation, has not always been around. Successful evangelists such as George Whitefield, Jonathan Edwards, and John Wesley never gave an altar call. In fact, they did not even know what it was. They invited their hearers passionately to come to Christ by faith and regularly counseled anxious sinners after their services. But they did not call sinners to make a public, physical response after evangelistic appeals. So where did the altar call come from? When did it begin?
HT: JT who also links to this post from Andy Naselli listing some resources on the altar call.