I am current a non-Italian resident who

https://finecobank.com/it/online/call Arezzo Agency 0575-353697 and ask mr. Lelli

YOU can ask for a tax code/codice fiscale from an Italian consulate.  

Modi is correct, log on to the consulate nearest you in the USA and it should have an area telling you how to apply, search codice fiscale (may be "tax code as Modi says). You certainly used to be able to do this.

In any case , for moving and buy , you necessity of a Codice Fiscale

Online , not - you has to provide some documents signed - IN ORIGINAL-, and shipped to Agency , via express mail service - but this is the only manner to have bank account - NO EXPENSES -  without go to Italy -  Other banks , provide you a standard non resident bank account - with expenses for deposit, drawing, via internet use ..and so on..  - If you need  Resident bank account , with lowest expenses , is necesary Italia Elective Residence .. you can find some info , at my website .>  http://www.lifeinitaly.it/Inglese/italyresidenceguide.htm

You can try INGdirect bank , its a very good bank

hm , at my knowing ,to  ING Direct  Agents in Italy , do not are allowed  , give bank accont to not italian , outside they's italian offices -

We are from the UK and recently opened an Italian bank account. You need your Code Fiscale and found that it wasn’t possible to open one on line. So we made an appointment at a large branch of a bank in a city (hoping that there would be someone who spoke English). The process took several hours and we nearly had to give up because we didn’t have an Italian phone number, but somehow we succeeded in the end. 

I should mention that we used Intesa Sanpaolo and have been very impressed. 

So , if you have problem  in having Italian bank accont from your's contry , without go o Italy , i can provide it to you ! , need only Copy of Passport and an apostilled  proxy , to provide Codice Fiscale, Bank account , Italian Phone card  - and one working wek - I make it , for all my clients , from several years .