Yes, you can contribute to a traditional IRA up to the annual limit even if you participate in a workplace plan, the rules and contribution limits are separate. However, depending on your income and marital/filing status, you might not be able to take a tax deduction for the contribution. See here.
https://www.irs.gov/retirement-plans/ira-deduction-limits
If you make a non-deductible contribution to a traditional IRA, that will create a "basis" in the IRA, this is an amount of already-taxed money. Your tax return will include a form 8606, and you need to keep a copy of this form for your entire life (it's an exception to the rule that you can throw away most tax papers after 3 or 7 years). If you make more non-deductible contributions in the future, you will use the prior form 8606 to prepare your tax return which will include a new form 8606 that tracks your total non-deductible basis. When you start withdrawing from the IRA, the fact that part of the balance was already taxed means that part of the withdrawal will be tax-free, as long as you have all your form(s) 8606 to prove it.
