Can the real time operating system used in aviation equipment be certified by itself?
A DO-178C compliant RTOS (such as LynxOS-178 mentioned by @mins) is going to have a certification package you provide along with your DO-178C artifacts for your software.

Note that there is no such thing as a DO-178C "certificate". DO-178C is a process that generates certification artifacts that are packaged and provided to the Certification Authority as part of some approval application (TSO, TC, STC, PMA)

It is also usefull to recognize that most software on equipment installed on an aircraft is not going to run on an RTOS, but rather run directly on the hardware (bare metal)