Does minecraft has infinity map?

Technically… No. But its enormous, I think around 299999999999 Blocks before you hit the border… And that's just talking radius.

Depends on which platform and version you are playing it on.

The latest PC version has an infinite Overworld map.
The XBOX 360 and PS3 editions have a 862x862 block overworld.
The PE edition has a 256x256 overworld.

Incidentally while the PC map is infinite, there's an invisible wall at 30,000,000 blocks from the spawn. The world continues on from that, but you can't walk past the 'wall'