My wife is a recent, legal immigrant to the US. I am considering
getting her a credit card. I know this may be difficult because she
has no credit, but I might be able to work something out with my bank.
Make her a designated user on one of your credit cards. That will start building her credit history. Then after a year or two get a card in her name only.
My question is, should I? Once she has a card, her social is in the
computers of Experian and other scumbags. If she's off the books, her
identity presumably cannot be stolen.
Now if the goal is to protect her social security number from ID thieves, there are other places where the SSN has to be supplied. Places include: applying for a passport, health insurance, getting a drivers license, getting a job, filing income taxes.
Any of these activities expose and store the SSN.
Even your activities can expose it. If you apply for a job that requires a government background check. They will ask for your spouses information, which can then be stolen.
In June 2015, OPM discovered that the background investigation records
of current, former, and prospective Federal employees and contractors
had been stolen. OPM and the interagency incident response team have
concluded with high confidence that sensitive information, including
the Social Security Numbers (SSNs) of 21.5 million individuals, was
stolen from the background investigation databases. This includes 19.7
million individuals that applied for a background investigation, and
1.8 million non-applicants, primarily spouses or co-habitants of
applicants. Some records also include findings from interviews
conducted by background investigators and approximately 5.6 million
include fingerprints. Usernames and passwords that background
investigation applicants used to fill out their background
investigation forms were also stolen.