I would recommend Integromat (similar but more flexible than Zapier) - probably using a trigger based on the new modified date / time field as described in my blog post:
Except you could use a Twilio connection to send an SMS instead of send an email.
It’s probably only a two-step process in Zapier. Step one is the “New Record in View” Airtable trigger (targeting a view in your table that only shows applicants marked as “Pending”). The second step would be the texting API. Zapier has its own “SMS by Zapier” integration that should do the job. Using the data gathered in the trigger step, you fill in the fields required by the SMS action.