Yes, of course. In fact, it's very common to say it that way.

That is exactly what I would say myself.

"I'm waiting a delivery" - In this sentence, "a delivery" is the direct object, but wait is an intransitive verb so it cannot take a direct object. "to wait for" is what's called a phrasal verb (a verb that is used with specific other words). In this case, the word "for" follows wait, followed by the direct object.

There is another verb "await" that is transitive. So you could also say "I'm awaiting a delivery."