There has been some discussion in the "Armory - Discussion Thread" on how to setup Armory to work while Bitcoin Core runs through Tor. However, it has kinda gotten lost in the mountain of information there. I've noticed some more questions about this subject pop up and thought I'd post a how to here.
Tor Browser Bundle setup:
1) Download and extract Tor Browser Bundle (no need to change any settings, you can just run Tor Browser Bundle as default)
Bitcoin Core setup:
1) Download and install Bitcoin Core
2) Run Bitcoin Core
and deselect "Map port using UPnP" and select "Connect through SOCKS proxy".
3) Make sure you settings match these: (Proxy IP: 127.0.0.1, Port: 9150, SOCKS Version: 5)(replaced with some lines in bitcoin.conf to make setup easier)
4) Close Bitcoin Core and wait for the "Bitcoin Core is shutting down..." message to disappear
5) Navigate to the bitcoin data directory (if you don't know where this is look here:
https://en.bitcoin.it/wiki/Data_directory)
6) If bitcoin.conf doesn't already exist, create a text file and rename it to bitcoin.conf. (You may have to show file extensions to make sure you didn't accidentally name the file bitcion.conf.txt. For windows users follow these steps to show file extensions:
http://malektips.com/windows-7-view-file-extensions.html#.U4Dxk1PLfN4 *If you are using a Mac see note below.)
7) Add this code to your bitcoin.conf file:
bind=127.0.0.1
port=8333
upnp=0
proxy=127.0.0.1:9150
Armory setup:
1) Download and install Armory
2) Open Armory and navigate to File, Settings, Privacy Settings. Then select "Enable settings for proxies/Tor"
3) Close Armory
Now to run Armory while Bitcoin Core runs through Tor, simply start Tor Browser Bundle,
Bitcoin Core, and Armory!
Let me know if you have any questions, or if this setup does not work for you!
WARNING: This setup does not guarantee complete anonymity from Armory, but all external Bitcoin Core traffic should run through Tor.
Edit: Removed Bitcoin Core from the list of programs to run since Bitcoind is automatically run in the background by Armory.
Edit 2: Replaced listen=1 with port=8333 in bitcoin.conf as "port=" serves the same purpose as "listen=" but only listens on port 8333.
Edit 3: Added information involving bitcoin.conf to help Mac users (courtesy of NewBTCGuy).
Edit 4: Changed various instructions to reflect changes in Bitcoin Core and Armory.
*For Mac users:
Answer for those who come after me (thanks to key help from picobit):
The Mac OS text editor is setup to operate with rich text and if one changes the bitcoin file extension to .conf from .rtf it won't change the format of the content. Thus one must:
1. Set TextEdit for plain text in the New Document pane of TextEdit preferences AND...
2. Open the Save dialog, choose Customize Encoding List from the drop-down menu for Plain-Text Encoding, add Western (ASCII) as an option, and choose that option for saving the bitcoin.conf file in Users/<Username>/Library/Application Support/Bitcoin