I agree with Luc, it does not appear to be possible.
In the full version of Publisher (2013) you set the page size in the Design tab > Customize group > Slide size drop down. That command is not available in the Web App. It appears MS assumes that everyone uses landscape screens. Not true, since I'm posting
this reply from a portrait screen <grin>.
The only possibility I could think of would be to start from a portrait template, but I don't see any way of providing custom templates to use in the Web app. Sorry.
So Luc's suggestion of creating the Portrait file on a full copy of PowerPoint then uploading it to skydrive and using the web app to edit it from then on.
If you don't have access to a full copy, I can post a blank file if you tell me which template you want to use.