It depends: In Italian there are only female and male as grammatical gender. So if you have an object (English it) which is female in Italian you can use the sentence in the way you proposed. Quale è la tua macchina? È la terza. BUT if you speak about an object which exists only in the male gender you cannot use this sentence. Quale è il tuo posto? È il terzo.
My thought went to someone asking the date. Che giorno e (is) oggi, o che cosa e la data Oggi? La data is feminine, so I would think the above response in english would be correct using 'it is the third'. Couldn't try it because my test question had me say the italian which was written.
In English, there is a subtle difference between "she is the third" and "she is third." The former implies a temporal sequence (e.g. "How many people have asked?" "She is the third."). The latter implies a ranking or position (e.g. "Is she the winner?" "She is third."). In Italian, do "È la terza" and "È terza" convey the same kind of difference?
"È" can be he/she or it. That doesn't help so you have to look elsewhere. In this case, it's "la terza". Since "terza" ends with an "a" (there are always exceptions), that means feminine and thus the feminine article "la". So that means "È" cannot refer to he, so it's either she or it. And, technically, the phrase can either be "She is the third" or "It is the third", as long as the "It" that is referred to is a feminine object. In most cases, the understanding would most likely be "She". Therefore, "She is the third".
A little long-winded, but hope it helps. :)