Is ideal gas incompressible?

All gases, including ideal gases, are compressible. That's because the molecules of gases are far apart and can readily be brought together by pressure. The specific heats of gases depend on the process. For an ideal gas, $C_p$ and $C_v$ are the specific heats for constant pressure and volume processes, respectively, and are related by the equation $C_{p}-C_{v}=R$.

The molecules of liquids and solids are packed very closely together making it difficult to compress them. Only one specific heat is usually specified for a liquid or solid.

Hope this helps.

The state equation of an ideal gas $$pV=nRT$$ clearly shows it Is compressible.

Even more - infinitely compressible.