Can a celiac eat pasta, pizza, and gelato? Is a trip to Rome even possible?
First, learn the basic phrase for without gluten — “senza glutine” (sen-za glue-tea-neh) in Italian. While there are many dishes that do not include gluten, such as rice dishes, cross contamination can be a problem so it’s a good idea to explain that you have an allergy. Celiacs is “celiachia” in Italian and the “ce” at the start of the word is pronounced as a “chay” so it’s “chay-lee-ah-chee” but you can show the restaurant this phrase from Celiac Travel which explains that you have celiacs and that you cannot eat food made with wheat or wheat products.
Sono affetto da celiachia (intolleranza al glutine), devo seguire una dieta assolutamente priva di glutine.
Qualsiasi cibo contenente farina/amido di grano (frumento), segale, orzo, avena, farro, spelta, kamut e triticale può causarmi gravi malori.
Luckily, the Italians are obsessed with gut health, so they will feel the tragedy for you, and they will understand. Now, on to the places in Rome where you can eat!

Restaurants:
Mama Eat Lab (100 percent gluten free) – They also have another restaurant called Mama Eat but it is not 100 percent gluten-free.
New Food Gluten Free – Ponte Sisto (100 percent gluten free)
Ristorante Pizzeria Il Veliero
Risotteria Melotti — it is a rice based restaurant
Pub Cuccagna
Ristorante II Viaggio – gluten and dairy free.
Millennium
Mangiafuoco Pizza & Grill
Taverna Barberini
Bakeries:
Pandalì
Celiachiamo Lab (also a shop)

Gelato:
Grom
Gelato G Italiano
Icecream Shop La Strega Nocciola

Read a really good article here. Much of this list is from that site (which includes information about AIC — gluten-free accreditation). This site also rates the places. I also looked at this site which gave a good roundup of gluten-free eats in Rome but more importantly, a list of gluten-free eateries at the airport!