If you're getting traffic spikes on a WordPress website, switching to nginx is probably not the first thing you should do.
The first thing to do is to install some WordPress-specific caching mechanism. My favorite is the W3 Total Cache plugin. This will help you by creating static cached pages of your site which Apache can serve much faster to anyone who isn't a logged in WordPress user.
It also has a lot more features, including memcached support, database and object caching support, CDN support, and many other potentially confusing things, but you don't have to set those up immediately. Just doing the static page caching will help a lot if you aren't already doing it.
If you're already caching as much as you can through solutions like this, then it might be appropriate to consider switching to nginx, upgrading your server, etc.