How about a screw type compressor or roots supercharger style compressor?
How much air are we talking about and how much pressure and temperature? how fast a is your 'rotary motion'? Those will be a MAJOR factors in choosing the right type of compressor for your application...
pressure ratios of 3:1 and high shaft speeds, go with a centrifugal compressor such as is found in turbochargers... they can even be compounded to provide higher pressure ratios.
very low speed compressors? I'd go with a diaphragm type
Medium speed? I'd go with a piston type
higher speeds, low pressure? something like a supercharger
higher speeds and pressures? screw compressors