If they want to upload a resume instead of filling out the data on the site, that could end up being a fairly big undertaking if you want to be able to parse the uploaded file into separate data elements. First you need to be able to read the file (e.g., will you allow MS Word files, and if so which versions?). That could be problem enough, but then you need to figure out how to extract the data you want from a text/mark-up structure over which you have no control, then develop some way of parsing it and identifying that data.
What I have seen, however is both: the user fills out the structured data via the web site forms, and then also has the option to upload their own resume in whatever file types you want to accept (.doc, .pdf, or whatever). The resume is stored but not searchable on-line, but prospective employers can download it if desired when their initial searches have given them a narrowed down list of candidates.