I have not received 1099 misc for doing surveys. Made $1600 which is less than standard deduction. Can I file without it?

Yes, you can file without a missing 1099-MISC (which may never have been reported to the IRS in the first place).

If you know the amount, however, you might want to report it on your return as if it were cash income not reported on a 1099-MISC). This way you can claim the expenses you incurred in generating the income (travel, supplies, equipment, cell-phone service, etc.).

If the 1099-MISC appears later on (e.g. in the mail or by way of a notice from the IRS), you won't have as much work to do in updating/amending your taxes. You can tell the IRS that the income was already reported and tell them where.

(As a practical matter, it is extremely common to omit reporting a Form 1099. You file before they arrive, they get lost in the mail, get lost in your house or get tossed along with junk mail).