Since WordPress is licensed as GPLv2, you can license any addition (i.e. theme) with a license that's compatible with version 2 of the GPL. Now here's the unfortunate part ... version 1 of the aGPL is not compatible with any version of the GPL. Version 3, however, is compatible with GPLv3 ... but not GPLv2.
Short answer: no, you can't license a WordPress theme with aGPL because neither version of the aGPL is compatible with WordPress' license (GPLv2).
Link to license compatibility chart for reference ...
Strictly speaking, yes. WordPress themes are considered derivative works, so they must be licensed in a fashion compatible with the core project. WP is licensed as GPLv2+, so you can (if you want to) upgrade it to GPLv3 for distribution.
That's important, because the only version of the aGPL that's compatible with the GPL is version 3 ... so your theme must be aGPLv3.
That said, you're under no expectation to redistribute WordPress on your own ... I'm just pointing out the compatibility here. But to keep things simple, I will always advise against using the aGPL. In practice, it doesn't lend well for WordPress themes (feel free to ask me why, but that's beyond the scope of this question).