ITIL is just a base set of rules. It is not poored in concrete so you can apply some of there rules onto OSTicket.
Don't do it the other way around.

ITIL as bernardflach stated is just a set of standard and guidelines. osTicket allows for the multi level ticket tracking. The few things that osTicket will not facilitate (yet- i still hope for asset tracking will be added) is the concept of the CMDB. In addition, much like quite a number of other ticketing tools, you will need to manually track the ticket types (ie. Track incidents and then manually run reporting to properly identify problems). Another concept which osTicket DOESN'T facilitate is the Incident to Problem transition.