Preheat the oven to 375 degrees F (190 degrees C).

Beat butter, white sugar, and brown sugar together in a large bowl with an electric mixer until light and fluffy. Add eggs one at a time, beating well after each addition. Beat in vanilla.

Stir together flour, baking soda, cinnamon, and salt in a separate bowl. Gradually add flour mixture to butter mixture and mix until blended. Mix in oats and butterscotch chips until combined.

Drop dough by teaspoonfuls onto an ungreased cookie sheet.

Bake in the preheated oven until the edges begin to brown, 8 to 10 minutes.