Learn Spanish (Latin America): Oigo un ruido en la casa.

Yes! The dictionary form of "to hear" is oír. In the present tense, its "I" (yo) form is completely irregular: oigo. This fits perfectly into a group of common Spanish verbs that have a special "-go" ending just for the first person, similar to hacer (hago) or poner (pongo).

Could I use escucho instead of oigo in this sentence?

It would change the meaning. Just like in English, there is a difference between hearing and listening. Oír means "to hear" (a passive action, like suddenly noticing a sound). Escuchar means "to listen" (paying attention on purpose). Since a noise (ruido) is usually unexpected, oigo makes the most sense here.

Why doesn't the sentence start with yo (yo oigo)?

In Spanish, the verb itself tells you who is doing the action. Because oigo can only mean "I hear," adding the pronoun yo (I) isn't necessary. You generally only include it if you want to add strong emphasis, like "Well, I hear a noise!"

How do you pronounce oigo?