Is there a traditional IRA income limit?
No, there is no maximum traditional IRA income limit. Anyone can contribute to a traditional IRA. While a Roth IRA has a strict income limit and those with earnings above it cannot contribute at all, no such rule applies to a traditional IRA.
This doesn't mean your income doesn't matter at all, though. While you can make nondeductible contributions to a traditional IRA no matter how much money you earn, you are subject to an income limit for deductible contributions if either you or your spouse has access to a workplace retirement plan. These limits vary depending on which of you has a retirement plan at work.
Income limits for other types of IRAs
A Roth IRA is the only IRA that has a strict income limit for eligibility to make any contributions. While there are ways to "backdoor" money into a Roth IRA, such as by contributing to a traditional IRA and doing a Roth conversion, you can't put money directly into a Roth if your income exceeds the annual cap.
Traditional IRAs don't have this rule -- nor do other types of IRAs, such as SEP-IRAs and SIMPLE IRAs, which are commonly used by self-employed people and small business owners. You can contribute to a SIMPLE or SEP-IRA no matter how high your income is, provided you meet the eligibility requirements for these account types.