By definition, "today" can never be a time in the past. The present perfect is a present tense -- that's why it's called the present perfect -- and describes the present.
That is, it refers to the result of a previous action.
"I worked today" is just part of a story: "I worked today, and then I went home, had a meal, watched TV..."
"I have worked today" means: "I don't need to work any more." Or: "I am tired."