日本語を学ぶ (nihongo o manabu)
* 日本語 (nihongo): Japanese language
* を (o): particle marking the direct object
* 学ぶ (manabu): to learn (formal and relatively polite)
You could also use:
* 日本語を勉強する (nihongo o benkyou suru): This is also very common. 勉強する (benkyou suru) means "to study," and is slightly more informal than 学ぶ (manabu). This translates more directly to "study Japanese."
Both are perfectly acceptable and widely understood. The choice depends slightly on context and desired level of formality.