I rang for pizza?
How do you say?
I telephoned the pizza restaurant and ordered a pizza.
I called and ordered a pizza to be delivered.
I called and told them to bring me a pizza.
I phoned the pizza place and asked them to bring a pizza.
There are many other ways to phrase this and much will depend on how formal you want to be. In addition, the way this is said will depend on what the local customs are - some will say, "I want a take-out pizza", and some will say, "I want a pizza delivered".
As Gill mentioned, there are many different ways to describe this situation. Probably the most common and succinct would be simply "I called and ordered a pizza." (This statement, however, does not clarify whether the caller is going to physically go and pick up the pizza or the pizza is going to be delivered to his home.)