Alonso was in the lineup and hitting third for Triple-A Albuquerque on Thursday.
The Chicago White Sox released the 32-year-old in early July after designating him for assignment on June 28. He was in the final season of a two-year, $16-million deal that included a team option for 2020.
Alonso accrued a .576 OPS in 67 games with Chicago, coming off back-to-back seasons with 20-plus home runs, including a career-high 28 in 2017.
The former All-Star has suited up for the White Sox, Cleveland Indians, Oakland Athletics, San Diego Padres, and Cincinnati Reds during his 10-year career (1,018 games).