The law of Washington is probably typical. Under RCW 9A.56.110,
"Extortion" means knowingly to obtain or attempt to obtain by threat
property or services of the owner, and specifically includes sexual
favors.
By RCW 9A.56.130(1),
A person is guilty of extortion in the second degree if he or she
commits extortion by means of a wrongful threat as defined in *RCW
9A.04.110(25) (d) through (j).
Then looking at the relevant definition of threat (please note that there is a numbering error in the statute, that should be (28), I don't know if they will fix it), it says
(28) "Threat" means to communicate, directly or indirectly the
intent:...
(e) To expose a secret or publicize an asserted fact, whether true or
false, tending to subject any person to hatred, contempt, or ridicule;
or
(f) To reveal any information sought to be concealed by the person
threatened;
Second degree extortion is a class C felony. It is not first degree extortion, since that requires the threat to be
(a) To cause bodily injury in the future to the person threatened or
to any other person; or
(b) To cause physical damage to the property of a person other than
the actor; or
(c) To subject the person threatened or any other person to physical
confinement or restraint;
Washington does not include a category of rape by extortion, though I've heard rumors that there is such a crime in some states. (It is not rape by forcible compulsion, second degree rape, because forcible compulsion is defined as "physical force which overcomes resistance, or a threat, express or implied, that places a person in fear of death or physical injury to herself or himself or another person, or in fear that she or he or another person will be kidnapped": that is, there has to be actual or threatened physical force)