You can transfer in those shares in lieu of cash, and they are marked for value at the closing price of the day. So make sure you don't transfer in more than what your annual contribution would be.

What this means though is that you can only do that for this year's contribution.

If you have shares in an IRA, then when you convert to a Roth, you will be paying tax on their market value at the close of the day you do the conversion.

But, the only way to transfer large numbers of shares from your regular account to an IRA is to buy in one account, and sell in another. And, since odds are you're at a loss, there's a wash sale rule to deal with.