There is no special entrance exam for instrumentation engineering. IIT Kharagpur offers it and that is through JEE Advanced. You have to qualify in JEE Main first to appear for JEE Advanced. HNB Garhwal University Srinagar (Garhwal) is another one that offers this through JEE Main. 

Most states have some universities or colleges that offer the branch. If you tell me which state you belong to, I can get back with exact details.