Yes. All you need to use AstroPrint is a device that has a web browser. This means that any smartphone or any tablet (android or iOS) will work with AstroPrint. Also, any regular computer (apple or pc) can use AstroPrint, without the need to download software onto the machine.
You just open your web browser and go to AstroPrint.com, or to AstroBox.local and you are in business.