Answer
Encephalitis is a symptom rather than a disease itself, the term encephalitis means an inflammation of the brain (-itis means inflammation, think about tonsilitis, arthritis etc). So your question would be better phrased "Is encephalitis caused by a virus?".
There are many things which can casue encephalitis some viruses which cause it are;Many human herpesviruses; rubella; mumps; measels; 'flu viruses; enteroviruses and some tick or insect borne viruses (e.g. West nile virus). Bacteria may also cause it (listeria, meningococcal, mycoplasma and pneumococci) as can some parasites (malaria and toxoplasma). Encephalitis may also be casued by non-infectious routes such as adverse drug reactions or auto-immune responses.
The term Arbovirus is a "catchall" created as a shortening of the terms arthropod-borne virus, this is not a specific virus rather a group of all insect borne viruses some of which may cause encephalitis.