First, what exactly is involved in this particular robotics degree? Is it an engineering degree? Computer science? Unfortunately, a degree in robotics is not as well defined as some other more traditional degrees...
Also, what kind of school is it? What kind of accreditation? What kind of reputation does the school have? All of those things will make it easier or harder to get that first job.
But, having said that - the skill set necessary for robotics can be applied in any number of industries. Industrial robotics is an obvious choice. Lots of work being done in bio-medical areas - from replacement limbs to rehabilitation devices. The auto industry is moving towards self driving vehicles - robotics skill set, right? Aerospace too.
What do you see yourself working on? (Probably one of the hardest questions to answer for most students when you really don't know what your options are and what the jobs will really be like.)