Stockpile cannot DRS transfer, but they can transfer to another broker for a $75 fee. The $75 has to be in your Stockpile account when you initiate the transfer.
If you do a full account transfer, be sure to download copies of all your documents as you will not be able to access them afterwards.
A popular choice is Fidelity, who can DRS transfer for free, and quickly. Fidelity will even reimburse the $75 transfer fee if you ask.
Stockpile to Fidelity Route:
Open an account with Fidelity. When it asks you how you want to fund your account, select "Transfer from Another Brokerage". You may need to supply a recent Stockpile account statement. Fidelity will pull your shares from Stockpile. This will take roughly 3 days. From there you can follow the Fidelity guide located here.