It depends, but it is possible. If you can contribute to a 401K or other qualified employer plan, your deductible IRA contributions may be limited or reduced to zero if you have higher income. The rollover you mention in your question does not raise your adjusted gross income, but it's possible your income was already too high to qualify. You are still allowed to contribute to your IRA, but you cannot claim a tax deduction for the contribution. It will act similar to a Roth IRA in this regard (that portion is not taxable when you take a distribution). Here is an FAQ on this subject: https://ttlc.intuit.com/replies/3301534
The caveat is that if you have both Deductible and Non-deductible IRA contributions, you want to keep track of the original amount you contributed to each so that the taxable amount can be determined. (You pay tax only on the deductible IRA distributions and not the nondeductible distributions). Form 8606 is used to report this. Here is an additional FAQ with more information on this subject: https://ttlc.intuit.com/replies/3300280
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