INDIANAPOLIS—Jennifer Fleming was convicted of dealing drugs in 2012, but when she gets out of prison next year, she is hoping for a job in computer coding.

“Technology is definitely going to be a steppingstone in keeping myself stable,” said Ms. Fleming, who is one of eight women in a pilot program at the Indiana Women’s Prison that officials plan to roll out to other prisons in the state. Ms. Fleming, 40 years old, passed a test and two rounds of interviews to be accepted into the program.

The...