The short answer is no, you cannot claim yourself as a dependent on your tax return. This is because you are considered to have your own personal exemption.
The IRS defines a dependent as a qualifying child (under age 19 or under 24 if a full-time student, or any age if permanently and totally disabled) or a qualifying relative. A qualifying dependent cannot provide more than half of their own annual support.
The child must be: (a) under age 19 at the end of the year and younger than you (or your spouse, if filing jointly), (b) under age 24 at the end of the year, a full- time student, and younger than you (or your spouse, if filing jointly), or (c) any age if permanently and totally disabled.
The rule is that if someone ``can'' claim you as a dependent, you must check the box. It is not, did or will someone claim you as a dependent. There is nothing that requires your parents to claim you as a dependent if you qualify, they will just be giving up a $500 credit (potentially).