After spending time with Curie roaming the wasteland, she will talk to you and tell you about her plans to become human. The person who can help her is Dr. Amari in the Memory Den. However, you have to complete the story quest “Dangerous Minds”. Bring her to the doctor when ready.
Dr. Amari will suggest getting synth brain for the procedure and will contact the “caretaker” of one her brain-dead synth patients. Curie will leave your party temporarily and you’ll have to wait for 24 hours for the quest to progress. You can just sit in the couch in the lab then wait for 24 hours.
If you’re a member of the Railroad, you’ll be familiar with the Caretaker. Convince the caretaker through a charm speech check to proceed with the operation. The quest will be complete shortly after the successful operation. Also, make sure to loot the items you may have given Curie’s old body prior to the operation. Now, you’ll be able to give Curie equipment and weapons like a standard companion.