Plugin

This can do that

http://wordpress.org/extend/plugins/contact-form-7/

Yes, it does have option to upload a file, just generate the field using “Generate Tag” option. For example, here is the site using Contact Form 7 with file attachment:

http://startupcms.com/support

You can even create as many upload inputs as you want.

You can find the docs at

http://contactform7.com/docs/

You are welcome, have a nice day!