Cyborgs are most times described as fictional or hypothetical creations. I've watched different kinds of movies where cyborgs exhibited different kinds of behaviors that can only be attributed to the emotion in them, while in some movies, cyborgs are emotionless. However, cyborgs that have emotions are first humans before they have a part of their bodies replaced with a kind of technology. Since humans are naturally emotional beings, the fact that they are part of machines does not mean that their emotional abilities have been reduced to remove completely.
A cyborg created in this form will still feel disappointed, loved, and happy if an action that will induce this feeling is created. On the other hand, cyborgs that are created in movies can be emotionless since they are completely mechanized but with the human look. Also, some cyborgs that are created in movies can have feelings if the creator has put a particular program that will make them emotional.
The correct answer to this question is Yes. Cyborgs do have feelings; at least some of them do. A cyborg is a human who has its entire body or part of its body taken over by electromechanical devices. One could argue that is that at the core, a cyborg is still a human, that it will have human emotions and feelings.
In many films like Blade Runner and Ghost In The Shell, cyborgs are seen as having emotions, such as loneliness. Though cyborgs are mainly known for being featured in movies, there are real-life cyborgs that have been created through science.