How do I scale i3 window manager for my HiDPI display?

Since version 4.13 i3 reads DPI information from Xft.dpi (source). So, to set i3 to work with high DPI screens you'll probably need to modify two files.

Add this line to ~/.Xresources with your preferred value:

Xft.dpi: 120

Make sure the settings are loaded properly when X starts in your ~/.xinitrc (source):

xrdb -merge ~/.Xresources
exec i3

Note that it will affect other applications (e.g. your terminal) that read DPI settings from X resources.

You can run xrandr as any user running an X session. Xrandr is a command line program, so you run it in your terminal.

So you would run something like this in your user terminal

$ xrandr --dpi 220

If you only want to change the DPI within i3, you could put the command in your i3 config file with the line:

exec xrandr --dpi 220

Depending on your distro you will find the config file in different places but often under ~/.config/i3/config