The short answer is no.  Reincarnation is not true.  The Bible states clearly that all men die and then they are judged.

Heb 9:27  And as it is appointed for men to die once, but after this the judgment,

There is no room for coming back repeatedly living many different lives.  Man does not have an immortal soul; see “Do you have an immortal soul?”  But we die once; see “What are the two deaths?” And there is hope of a resurrection to eternal life; see “What are the three resurrections?”.