As far as I'm aware, there is no way to do that through TurboTax.
There is an IRS Refund Tracking Number listed toward the end of this article.
https://www.irs.gov/uac/checking-the-status-of-your-refund
You can track your refund on your smart phone through these sites. They will let you know if the IRS got your return and approximately when you'll receive your refund!
https://turbotax.intuit.com/tax-tools/efile-status-lookup/
https://www.irs.gov/refunds