Many fonts on Typekit support Italian. You can browse fonts that support Italian by selecting "Italian" from the list of supported languages in the sidebar under browse fonts.
Italian is included in the default option, so the Italian characters will be available to your website within a few minutes of publishing your kit.
You may also create a custom language subset which includes Italian, to reduce the size of your kit. The Language Support & Subsetting help page has more information on the character set options.
All fonts that support Italian include the following letter characters, at minimum: