When answering a question such as this one, it is first useful to find a working definition as to what the quality of ruthlessness entails. The Cambridge English Dictionary defines it in the following manner:
the quality of not thinking or worrying about any pain caused to others when deciding what you need to do.
To be ruthless, then, involves a single-minded pursuit of one's goals, uncaring of the impacts your actions would have on others. With that in mind, the character of Macbeth is almost certainly ruthless, and to an extraordinary degree at that.
When Macbeth opens, he is already a Scottish lord, but the play's first key turning point can be found in act 1, scene 3, in which Macbeth and Banquo encounter the witches, who make the prediction that Macbeth will be king. In the proceeding events, we see his ruthlessness in action, as (with the assistance of his wife) Macbeth seizes the throne through force, murdering Duncan when he arrives to stay at Macbeth's castle. This is the great crime around which the action of the play hinges, and, in and of itself, it would qualify Macbeth as not only ruthless, but actively villainous in his characterization.
However, you can find other examples as well. For example, at the same time that the witches predicted that Macbeth will become king, they also make the prediction that Banquo's descendants will reign as king. Macbeth responds to this prediction by ordering the murder of Banquo and his son, Fleance, seeking to prevent this prophesy from coming to fruition (while Banquo is killed, Fleance escapes his would-be killers). These are only a few the examples that can be used to assert Macbeth's ruthless nature.