can we use category in profile

There are a few modules that come to mind like Taxonomy User and User Tags but I don't have any experience with them and can't say more. Perhaps someone who has used them can post their experiences?

You can also use something like Bio or Usernode to turn user profiles into nodes. Once a profile is a node, it can be assigned taxonomy terms just like any other node. There's a Profiles as nodes group you might be interested in.

Alternativey, you can use the core profile module to have something like tags but it doesn't use the core taxonomy module. Here on drupal.org, for example, each user has an Interests field in the user profile and users with similar interests is shown at http://drupal.org/profile/interest/Profiles+as+nodes).