Yes but you need admin rights.

Set up a profile first. Admin - Security Profiles - Select Project Profiles. Select Add button. Under Profile Name, name the profile whatever you want to call it "READ ONLY" or something similiar. You will notice in the details below this nothing is checked. If there is, uncheck the box. Select Close.

Admin - Users - select User Name. Under Project Access tab, select the Responsible Manager for that project. Then click in the Security Profile and a drop down will appear. Find the profile name you created and select it. Close the window. Press F5 key to refresh.

Make sure user is not logged in at the time and note that since P6 assigns project access by Responsible Manager/OBS and not by individual projects. For example, "John Smith" is the owner to 3 projects in P6. You need "Jane Jones" read access to one of those projects and write access to the others. With the way it is set up "Jane" has read access to all 3 projects. She cannot write to the other 2 projects. You will need to set up separate Responsible Owner/OBS profiles to give Jane the right access.