How to move the blinking cursor with the mouse in nano editor?

You can start nano with the -m (--mouse) option. From man nano

   -m (--mouse)
          Enable  mouse  support,  if  available  for  your system.  When
          enabled, mouse clicks can be used to place the cursor, set  the
          mark  (with  a double click), and execute shortcuts.  The mouse
          will work in the X Window System, and on the console  when  gpm
          is running.

Add this to your ~/.nanorc file

set mouse

This will cause the mouse to work every time you open nano

(source The GNU nanorc documentation)

This works in Ubuntu: hold Esc and press M while using nano, it'll enable mouse support.