Yes, the definitions still will be circular. However, the definitions point at each other in a certain special pattern. To find the special pattern, go look at the list at the top of this page. Electric charge is a component of atoms. In other words, after we have broken an object into molecules, and broken the molecules into atoms, when we break the atoms apart we discover particles of electric charge.
Charge is material, it is like atoms but it is one step lower than atoms.
Most science textbooks tell us that solid objects are made of atoms. It is also valid to state that solid objects are made of electric charge. Objects are made of equal quantities of positive and negative charge, and objects stay together because of the attraction between the quantities of opposite charge inside them. Chemical bonds are electrical in nature. Since matter is made of charge, all physical motion is a motion of charge, but both the negative and the positive move along as one.