Hi;

I'm a newbye and I'm owner of an Alfa Romeo Giulietta 1.6.

I need to raise up idle speed because at nominal rpm (820) the engine has an annoying vibration which disappears to 880rpm.

I have an OBDII ELM237 compatible interface bluetooth, can I use this to modify this parameter? What software can I use and what should I need?

There is no simple solution to your need, elm crap wont do anything to your iddle maps, you need to read the ecu with tuning tools and edit the iddle map/maps.