Why have marcellus and bernardo asked horatio to join them in their watch-guard atop the castle of elsinore?

The correct answer is:

They want Horatio to see the Ghost that has been walking at night.

Horatio was asked to go to see for himself if the story Marcellus and Bernardo had told him was true. They insist that on the past couple of nights, always exactly at the stroke of one, a ghost has emerged in the likeness of the late King Hamlet.