For a married person in the U.S. who wants to sponsor a foreign spouse to come to this country with an immigrant visa, the main criteria is having either U.S. citizenship or lawful permanent resident status. Beyond that, most of the immigration application process focuses on whether the marriage is the real thing and whether the would-be immigrant is actually admissible to the United States. The U.S. citizen or permanent resident's character or characteristics get very little scrutiny.
There's one major exception, however. Under the Adam-Walsh Child Protection and Safety Act of 2006 (the "Adam Walsh Act") U.S. citizens and lawful permanent residents (LPRs) who have certain criminal convictions cannot petition for family members to receive U.S. residence (green cards). (See I.N.A. §§ 204(a)(1)(A)(i) and 204(a)(1)(B)(i).)
(The same limitation applies to U.S. petitioners filing K-1 fiance visas.)
In other words, if a U.S. citizen or LPR with one of the relevant crimes on record submits USCIS Form I-130 to start the petition process, the government will in all likelihood deny it. U.S. Citizenship and Immigration Services (USCIS) runs criminal background checks on U.S. petitioners in such cases, to find out whether the FBI, sex offender registries, or a related agency have a record of any crimes.
If one of the crimes that are a problem under the Adam Walsh Act turns up, the foreign-born person might, as a result, be unable to immigrate via this marriage.
Broadly speaking, the category of crimes that will bar citizens and green card holders from petitioning for immigrants are offenses against a minor (someone under the age of 18). These include:
Foreign convictions also count for purposes of this law (with exceptions for cases where the defendant did not receive a fair trial).
Would-be U.S. petitioners who have anything remotely similar to one of these crimes on record should speak to an immigration attorney before filing an immigrant visa petition on a family member's behalf.
The law created an exception for instances where the Department of Homeland Security (DHS) determines, in its sole discretion, that the U.S. person filing the visa petition poses no risk to the beneficiary.
It's up to petitioner to not only ask for this exception, but to prove that he or she poses no risk, "beyond a reasonable doubt." That's a high burden of proof.
To successfully convince DHS, the petitioner will need to supply documentary evidence (preferably certified copies or signed affidavits) showing what happened and what the petitioner has done by way of rehabilitation. These might include, for example:
If the DHS is convinced that the petitioner poses no risk, the I-130 application can move forward. If not, this is the end of the line. There is no appeal from the DHS's determination.
It would be wise to get an attorney's help with this filing, to make sure it gets done right the first time.