My husband owes a offset for child support and I am a stay at home mom . We live in Illinois and I would like to know if I can file injured spouse to recvd eic back for my son.

You may be an injured spouse if you file a joint tax return and all or part of your portion of a refund was, or is expected to be, applied to your spouse’s legally enforceable past due financial obligations. To be considered an injured spouse; you must have paid federal income tax or claimed a refundable tax credit, such as the Earned Income Credit or Additional Child Tax Credit on the joint return, and not be legally obligated to pay the past-due debt; Special rules apply in community property states; If you filed a joint return and you're not responsible for the debt, but you are entitled to a portion of the refund, you may request your portion of the refund by filing Form 8379; You may file form 8379 along with your original tax return or you may file it by itself after you receive an IRS notice about the offset; You can file Form 8379 electronically. If you file a paper tax return you can include Form 8379 with your return, write "INJURED SPOUSE" at the top left of the Form 1040, 1040A or 1040EZ. IRS will process your allocation request before an offset occurs; If you are filing Form 8379 by itself, it must show both spouses' Social Security numbers in the same order as they appeared on your income tax return. You, the "injured" spouse, must sign the form; Do not use Form 8379 if you are claiming innocent spouse relief. Instead, file Form 8857. This relief from a joint liability applies only in certain limited circumstances. However, in 2011 the IRS eliminated the two-year time limit that applies to certain relief requests. IRS Publication 971, Innocent Spouse Relief, explains who may qualify, and how to request this relief.
Please follow instructions on irs website here. Tax Trails - Can I File an Injured Spouse Claim?