Not only is the concept of reincarnation not found in the Bible, the Bible shows that there is no immortal spirit and that the condition of the dead is one of inactivity - likened to a deep sleep. (Ps. 13:3)
“The living are conscious that they will die; but as for the dead, they are conscious of nothing at all.” (Ecclesiastes 9:5)
“He breathes his last breath, he returns to the dust; and in that same hour all his thinking ends.” (Psalm 146:4) “The New English Bible”
For much more, see:
REINCARNATION - Links to Information (INDEX; Watchtower Online Library)
Reincarnation (Search Results From the Watchtower Online Library)
Reincarnation (rs p. 317-p. 321; Watchtower Online Library)
Do You Believe That You Have Lived Before? (THE WATCHTOWER DECEMBER 2012; JW.ORG)