I was in high school January 2023 - June 2023. I also worked making $20,510. I lived with my parents. Can i let my parents claim me for 2023?

[DoninGA]

If you were under the age of 19 in 2023 or a full time student (which you were) under the age of 24, then your income is not a factor on whether or not your parent's can claim you as a dependent.  What is relevant is if your parent's provided over one-half of your support (which they probably did).  They should be able to claim you as a dependent under the Qualifying Child rules.

To be a Qualifying Child -

1. The child must be your son, daughter, stepchild, foster child, brother, sister, half brother, half sister, stepbrother, stepsister, or a descendant of any of them.
2. The child must be (a) under age 19 at the end of the year, (b) under age 24 at the end of the year and a full-time student or (c) any age and permanently and totally disabled.
3. The child must have lived with you for more than half of the year. Temporary absences while away at college are considered living with you.
4. The child must not have provided more than half of his or her own support for the year.
5. If the child meets the rules to be a qualifying child of more than one person, you must be the person entitled to claim the child as a qualifying child.
6. The child must be a U.S. citizen or U.S., Canada or Mexico resident for some portion of the year.
7. The child must be younger than you unless disabled.

[CatinaT1]

Perhaps.  A dependent must meet the requirements of a qualifying child or a qualifying relative in order for you to claim them on your tax return.  

Did you provide more that half of your own support during the year? That would be my only question.

The tests for a qualifying child are: 

Relationship: Must be your child, adopted child, foster child, brother or sister, or a descendant of one of these (grand or nephew). 

Residence: Must have the same residence for more than half the year. 

Age: Must be under age 19 or under 24 and a full-time student for at least 5 months. They can be any age if they are totally and permanently disabled. 

Support: The dependent must not have provided more than half of their own support during the year. 

Joint Support: The child cannot file a joint return for the year. 

The tests for a qualifying relative are: 

Qualifying Child: They are not the “qualifying child” of another taxpayer or your “qualifying child.” 

Gross Income: The dependent being claimed earns less than $4,700 in 2023. 

Total Support: You provide more than half of the total support for the year. 

Member of Household or Relationship: The person (a friend, girlfriend, non-blood relative) must live with you all year as a member of your household or be related to you. 

TurboTax software will ask you simple questions and give you the tax deductions and credits for which you are eligible based upon your answers. 

See also these TurboTax Helps. 

Who Can I Claim as a Tax Dependent? 

Rules for Claiming a Dependent on Your Tax Return