Yes, you may bring cash to a federal facility for deposit into your inmate trust account. We would recommend money orders though as it would have your name (and ID number "xxxxx-xxx") on the check and it won't get "lost".
https://www.inmateaid.com/ask-the-inmate/if-i-am-about-to-self-surrender-can-i-bring-in-money-to-fci-aliceville#answer
Accepted Answer Date Created: February 26,2016