Can my wife apply for social security spousal benefits?

Of course, you wife can apply for Social Security benefits, but she cannot restrict her application to spousal benefits only until she reaches her Social Security “full retirement age” (FRA). Because she was born before January 1, 1954, she will be allowed to restrict her application to spousal benefits, but she must wait until she has reached the age of 66 to do so.
If she were to apply before she reached age 66, she would be deemed as applying for all benefits to which she is entitled; in other words, both her own benefit and a spousal benefit, and she would be given whichever benefit was highest.

The rule John is quoting above is part of the Bipartisan Budget Act of 2015, which changed the rules for those born after January 1, 1954. The link for more information on this subject can be found at https://www.ssa.gov/planners/retire/applying6.html
As to your comment about your wife working, Social Security has an Earnings Test for those younger than their full retirement age (for both you and your wife, it is age 66) and for the year 2017, the earnings limit is $16,920. Meaning she can make up to that amount without her Social Security benefit being reduced. If she expects to make more than $16,920 in 2017, she might want to wait to apply for her Social Security until she either stops working or until her earnings drop below the Earnings Test amount. In the year she reaches her FRA, the limit is substantially higher.