"I have to clean the kitchen today."
Translation:Tengo que limpiar la cocina hoy.
Yes. The yo is correct, though not usually used. But the que is missing. It has to be tener que + infinitive to tell what one has to do.
Spanish has many phrases that don't translate literally into what they mean in English. (Phrases like this are called idioms.)
For example "tener que" means "to have to" even though it doesn't seem like it should. And "tener frío" means "to be cold." There are many more - we just have to get used to them. :-)
You can find more information and more examples here: https://studyspanish.com/grammar/lessons/tenexp