1. Leviticus 8:28 (ESV)
  2. Exposition

Were the priests allowed to keep the wave offering?

Leviticus 8:28 (ESV)

28 Then Moses took them from their hands and burned them on the altar with the burnt offering. This was an ordination offering with a pleasing aroma, a food offering to the LORD.

No, they did not keep any of it; they were required to return it all to Moses (Leviticus 8:28).