Yes and No.
Yes, they can take and cast find familar
The feat Magic Initiate reads:
Choose a class: bard, cleric, druid, sorcerer, warlock, or wizard. You learn two cantrips of your choice from that class's spell list.
In addition, choose one 1st-level spell from that same list. You learn that spell and, using this feat, can cast it at its lowest level. Once you cast it in this way, you must finish a long rest before you can cast it in this way again.
Find familiar is a First Level spell. If you choose the wizard spell list, then you can choose that spell, and be cast as described in the Feat. It takes only the casting time, and not the extra ritual time to do so.
Can't cast it as a Ritual
Unless they have ritual casting from their class or another source, they may not ritual cast the spell. You would have to be your single spell per day used through the feat, or a spell slot if find familiar is on your class list.