No, only an opponent can redirect damage from sources he controls to your planeswalkers. You can never redirect damage to your own planeswalkers with the planeswalker damage redirection rule.
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.
Can I redirect the damage it deals to me to a planeswalker I control?
Former Rules Advisor
"Everything's better with pirates." - Lodge
(The Gamers: Dorkness Rising)
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(Girl Genius - Fairy Tale Theater Break - Cinderella, end of volume 8)
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.