There is no statement to elect to treat a spouse as nonresident. If the US resident is not electing to treat the nonresident spouse as "Resident for Tax Purposes", then the resident will simply file as married filing separately reporting only their income on form 1040. The nonresident spouse with US income will file separately as well using form 1040NR to report US only income. In F1 status the income is not subject to Social Security.
If however, the couple elects to file a joint return then an election is made to treat the spouse as "Resident for Tax Purposes" as @DaveF1006 states. If that resident election is made then the income earned by the F1 visa holder is subject to social security taxes. (see reference below) and a corrected W2 or changes to social security withholding to capture the FICA taxes must be worked with the employer. The FICA taxes are not handled on the form 1040.
Here is social security exemption reference. (see the F1 visa...limitation).
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