In general, no. The planeswalker redirection effect given in the rules applies only to noncombat damage from sources a player controls to an opponent, not to that player himself or herself (C.R. 306.7). Therefore, if you control Mana Crypt as it deals the damage to you, C.R. 306.7 doesn't allow the damage to be dealt instead to a planeswalker you control. Nothing in the rules allows you to have any damage be dealt instead to a planeswalker you control, without more.
EDIT (Apr. 27, 2018): Edited to conform to rule changes with Dominaria.
EDIT (Jun. 6, 2018): Correctness edit.
EDIT (May 8, 2019): Edited.