This is pretty much one of the primary features of osTicket! Just go to Admin -> Emails -> Emails and set up the details for the mailbox you want monitored. You'd also want to consider whether you set up a cron job on the server, or use autocron, meaning the mailbox is only polled while an agent is logged in.
Once done, anything sent to the mailbox will be pulled into osTicket and processed according to any rules or filters you have set up.
