Obviously "moral inturpitude" is used by some people, but moral turpitude is the correct word to use when anyone wants to refer to "a vile, shameful, base person," or "a depraved act".
The following quotes were found in various places on the internet indicating that these people consider "moral inturpitude" as an acceptable usage
"Only a person of limited intelligence could misinterpret his words, or a person of moral inturpitude twist his words in such a disgusting manner to suit such low purpose."
"Establish license requirements for owners, operators, and employees to insure moral inturpitude in order to protect against sexually related crimes."
"I can see how moral inturpitude if in a trial that tells the truth or a history of violent crimes etc., could be a reason to restrict or monitor access, however I feel that closing the borders isn't the way to go."
"Then in the episode that aired on 2/29/06, they made a quip about a father being able to marry his own son in Massachusetts – alluding to the perceived moral inturpitude of the state allowing same-sex marriages.
". . . if you couldn't trust him the universe would implode as he is a mathematical constant, a pillar of moral inturpitude and friendship."