What type of doctor can order a compartment pressure measurement? Orthopedic doctor can do it?

Compartment syndrome. Measuring compartment pressure requires inserting a needle into a muscle compartment, and is usually performed by an orthopedic surgeon.
Any. That particular test usually involves insertion of a needle with a special gauge to interpret pressure into tha compartments of an extremity (for example, the lower leg has 4 compartments). It is usually performed on a somewhat urgent basis and is typically ordered/performed by orthopedic and general surgeons as well as primary care and emergency physicians.