Here's a breakdown:
* Ich: I
* verspreche: promise (verb in the present tense)
* es: it (referring to the promise itself)
Other options:
* Ich versichere dir: I assure you (more formal)
* Ich gebe dir mein Wort: I give you my word (more emphatic)
The best option depends on the context and the level of formality you want to convey.