Circuit or Equipment to delay high speed square clock signal?
Consider a programmable delay line or programmable timing element. These are ICs which can apply delays to a clock signal, and can be controlled by a microcontroller to vary they delay they apply.  

You will need to choose a chip based on the delay range and resolution you need, but to give an example, the Maxim DS1124 would be suitable for 10MHz clock signals, and con be programmed over SPI.