Can inverted microscope also be phase contrast microscope?
Definitely true, an inverted microscope is one where the optics are positioned below the specimen, and the light source above, providing an optimal situation for looking at a live culture. The Phase rings that shift the light come soon after the light source. For phase, the orientation doesn't matter, just the order:

Upright microscope

Orientation:

(top)eye--->objective--->specimen--->phase--->light source

order:

eye-->Phase compatible objective-->specimen-->phase disk-->light source

Inverted microscope

Orientation

(top)light source--->phase--->specimen---->Objective--->eye

order

eye-->phase compatible objective-->specimen-->phase disk-->light source

Not all microscopes have phase no, they are an important and expensive addition to a microscope. Adding phase not only required the phase disk but also a phase compatible objective.