At Empellón Cocina, a restaurant in New York City, diners see a not-so-gentle reminder at the top of the menu. "Empellón strongly discourages the use of cellphones, unless you're posting food porn on Instagram. #Empellon," it says in bold letters.

The aim is to get diners comfortable posting photos, says co-owner of the nouveau Mexican restaurant David Rodolitz, who came up with the tagline five months ago. "It's almost like they are becoming a brand ambassador on behalf of the restaurant," says Mr. Rodolitz. It also helps to bring followers to the restaurant's own Instagram feed, which informs users about specials or offers behind-the-scenes glimpses of the kitchen, he adds.

Establishments accustomed to viewing snap-happy smartphone users with annoyance are now realizing the potential of social networks to boost business. Some are trying to encourage restaurant-goers to post pictures of the food by promoting their social-media presence and courting Instagram users with off-menu freebies. Some restaurants, even those that frown on cellphone use in the dining room, are publicizing their social-media hashtags—words or phrases used to identify topics—at the table and encouraging diners to snap a photo before they dig in.

For many diners, a great restaurant meal now includes the obligatory food photo to show their social-media following where they've been. Instagram, owned by Facebook Inc., has legions of users who post photos of food, says David Gerzof Richard, professor of social media and marketing at Emerson College in Boston. While diners tend to rant about bad meals online, the beautiful pictures often seen on Instagram tend to overshadow any criticisms users may post, says Mr. Gerzof Richard, who also runs a social-media marketing firm.

Many restaurants and their publicists monitor their mentions on Instagram, Twitter and the like by searching daily for the restaurant name or hashtag.