You can easily import raster/bitmap graphics (such as PNG pictures) to Adobe Illustrator and work with them in your project. It's not actually png to ai conversion in file conversion sense, just picture import so you can use it as object.
But of course you might have been searching for a way to create a vector AI graphics from PNG image. This will require moderate knowledge of Illustrator and its functions, especially one called LiveTrace. This function basically allows bitmap to vector conversion, but requires that the person doing this tracing knows what he is doing.Open PNG file Open AI file
A powerful vector graphics editor from Adobe
A professional photo editor and manager for Windows
A set of applications used by professional graphic designers
A vector-based drawing software
Desktop publishing software