Peppermint Linux does not have a "arrange icons" setting for the desktop. A possible work around is to add a panel with your icons on.
Right click on the bottom panel, then click on create new panel.
Right click on the new panel, click Panel settings and go to the panel applets tab.
Add an application launcher bar, click edit and set it to the program you want
add a spacer between application launcher bars to give it a "justified" look.
Right click on the top panel, then click on panel settings, go to the geometry tab. Here you can set the icon and panel size. My panel is 22 pixels high and the icons are 20 pixels high as my eeepc has a 7" monitor and I do not want to loose too much space to a panel.
If you like to hide the panel (which I do not) go to the Advanced tab and click on the check box "Minimize when not in use"