How do I italicize fonts that don’t have an italic variant in Illustrator?

As KMSTR says, you don’t. Impact does not have an italic variant, nor a bold, for that matter.

Many consumer-based software like Microsoft Office allow so-called faux bold and italic for all fonts installed: if a separate font file for these alternate styles is not installed, the software simply slants the characters (for faux italic) or makes them thicker itself (for faux bold).

Do note that slanting is hardly the same as actual italics. Compare slanted and italic Garamond, for example:

Since faux is a way of obtaining these styles that the original type designer didn’t have in mind, it is widely viewed as ‘incorrect’ among typographers and designers. Hence, Illustrator (and other other Adobe applications) only allows it with an option that isn’t too easy to find or access.

You can use faux by different means, depending on the programme you’re using:

Illustrator: simply shear your text object.

Photoshop: In the Character panel, you can find Faux Italic in the panel’s options.

InDesign: Use the Skew option in the Character palette.