This question can be interpreted in two ways. If you mean “Do you round the cost of the item to the nearest dollar, and then compute the tax?”, then: No. The tax applies to the actual cost of the item, not a more-convient-estimate of the item’s cost.
If you mean “Do you compute the tax and then round the tax-included total to the nearest cent?” then: Yes – no merchant is going to charge you a fraction of cents.
So if your item cost $10.62, and tax in your state is 5%, the tax is 10.62 * 0.05 = 0.531. The total cost is therefore $10.62 + $0.53 = $11.15