Can I restrict faculty group users from accessing Aware?

Yes. As an admin you can choose the level of access that faculty group members have to the Aware console. You can choose partial or no access for any of the faculty group members through the Settings tab for a particular faculty group. 

If you unselect all options under ‘Select type of activity to show’, the faculty group members will not have access to the Aware console. 

However, if the same person is a part of multiple faculty groups and assigned to different Org. units, their access level will be determined by the settings for each of the faculty groups they belong to. For example, for Group A the access might be restricted to only activity summary on the dashboard, for Group B all three options might be disabled. In this case, the faculty group member will be able to access the Aware portal but see only activity summary on the Aware dashboard for the Org. units associated with Group A.

To set up faculty groups, read this KB article.