Can I apply for a variation order due to the delay of payments?

I believe this should be stated in the contract on the first place. I doubt that this is the case, as in Saudi Arabia they will not mention such terms. In a matter of fact, almost all contractors get delayed payments by clients "usually government projects" & no one can object to that!

A variation is a change in the contract required by the Client or by the contractor which might increase /decrease the scope, increase /decrease the time and increase /decrease of the cost of a project.

Delays in issuing payments affecting  the contractor financial and his  capability to continue working on the project  should be dealt as a contractual claim, it must be raised by the contractor for compensation (time, loss of profit, the increment of cost, etc, resulted from the client actions) this claim as per the conditions  established in the contract agreement