There's an English language Taobao web site. Is there an English language Taobao app for

a smartphone?

There isn't.

yes, there is. It's called Baopals. they also have a wechat site where you can shop. It's

taobao and Tmall in English. Not sure if they have an app. I use their wechat site.

@kongming There's no official taobao website in English as far as I know... Which one are you referring to?

i used the baopals website, and although nowhere near as comprehensive as the real thing, its got some good stuff, all in english, etc.
you can pay via wechat as of late, and it lets you follow baopals via wechat, where a page comes up with searching and account management,

allowing you to shop on your phone that way.