Can you A/B test with SMS?

Yes, but the limited space means fewer variables to test and more discipline required.

Test one thing at a time

The offer, or the wording, or the timing. Changing two things at once means you will not know afterwards which did the work.

Make sure you have volume

With a hundred recipients, the difference between three and five clicks is chance. Below a few hundred per variant, testing makes little sense — then choose on judgement.

Measure the right outcome

Not the click but what happened after it. A variant that produces more clicks but fewer purchases is the worse one.

Use separate links

One shortened link per variant, otherwise you cannot attribute the clicks.

What most often wins

Not cleverer wording, but a different time or a clearer offer. Start there before you start tinkering with vocabulary.