I have filed my Tax Return and am due a refund. I received a 1099-DIV on February 20th for $10.24, will I have to file an amended return?

No. It is too small to make a difference.

No, do not amend your tax return at this time.

You should always make every effort to include all of your income on your tax return.

However, I agree with ee-ea that it will not significantly change your tax.  

You may get the dreaded IRS tax notice. The IRS already has the 1099-DIV.

The IRS may recalculate your tax and reduce your refund by a couple of dollars.

At any rate I would not amend anything until this all washes out.