Does applying voltage means create a force on electron to move?
Voltage is more a property of a location in space or in a circuit than of an individual electron. It tells you how much energy it would take to move an electron (or other charged particle) to that location.
What causes a force on a charged particle is the electric field. But electric field is equal to the gradient of the voltage, so they are closely related.
if voltage is applied then elctrons will accelerate.
No. Only if there is a gradient to the voltage. Meaning if the voltage is changing as you move about in space. If the voltage is slightly higher "over there" than it is "here" then an electron will feel a force pushing it towards "over there".