As I understand it, osTicket wouldn't be able to send SMS texts itself, you have to use a broker and their API to submit messages to them. Sans a service like the now-defunct (teleflip).
Another option is a USB GSM modem (or telephone that will allow AT commands) with a valid SIM and a carrier who allows unlimited SMS, or very cheap SMS.
Some resources on that:
(Sending SMS Messages from Linux)
(How are you sending SMS alerts? (in regard to the excellent Zabbix monitoring software)
(Web service) (negates the local GSM modem)
(Another one)
(Another one)