Question:
Is it permitted for a Levi to marry a convert?

Answer:
Yes, it is permitted. The restriction against marrying a convert applies only to a Kohen and does not apply to a Levi. Accordingly, it is permitted even lechatchilah for a Levi to marry a convert. Furthermore, in such a case the children follow the status of the father. Therefore, any children born from this marriage are likewise considered Leviyim. Indeed, Moshe Rabbeinu—arguably the most famous and greatest Levi in Jewish history—married Tzipporah, who was a convert.

Sources:

See Michaber E.H. 8:3 “Leviyim, Yisraelim, Chalalim, converts, and freed slaves are permitted to marry one another. A convert or a freed slave who marries a Leviyah, a Yisraelit, or a Chalalah— the child is considered a Yisrael. However, a Yisrael, Levi, or Chalal who marries a convert or a freed slave—the offspring follows the status of the male.”; Rambam Issurei Biyah 19:16; Mishneh Kiddushin 69a