That kind of depends on how you define "human"
Archeological philanthropists are generally agreed that the more or less modern humans took shape about 200,000 years ago. At the time, there were other human-like apes with long names that I can never remember. It is impossible to tell exactly when and under which circumstances we evolved to use a complex spoken language, but the fossil record indicates that we began to make art by about 30,000 to 40,000 years ago. This is around the time the first cave paintings, ornate clothing, and Earth Mother statues start to show up. This is when we start to find evidence of complex societies with advanced aesthetic awareness and developed sense of religion.
In short, our direct ancestors show up in the fossil record about 200,000 years ago and evidence of uniquely human traits such as art and religion show up around 40,000 years ago at the latest.
"The human race" as we know it did not exist a million years ago, however, the ape species we descend from certainly did. As I said, it depends on your definition of human ;)