Yes. Quick version (assuming you want to replace the first male portrait):
1. Take the portrait you want (you probably want it to be in grayscale, but that's not essential).
2. Resize the portrait to 100x75 pixels (that's 100 in height, 75 in width) and convert to .png format.
3. Use the Fallout Tactics editor to convert the png into a .zar file (use the option marked "PNG TO ZAR").
4. Rename your new .zar file to "core_prefab1.zar".
5. Move core_prefab1.zar to the "14 Degrees East\Fallout Tactics\core\gui\char" folder (that is, the "char" folder nested inside the "gui" folder nested inside the...). If you don't see these folders, create them.
6. Start the game. Ignore the "large" portraits where you have the option of choosing a default character, and choose to create a new character. If you did everything right, your custom portrait should have replaced the first human male portrait.
core_prefab1, core_prefab2 and core_prefab3 are male portraits; core_prefab4 and core_prefab5 are female. If you want to change the portrait of your recruits, that's a bit more complex, because you'll need to know the filename of the specific portrait you want to replace.