'rejected' is the simple past tense of 'to reject' 'have rejected' is the present perfect tense of 'to reject' Whether you use the simple past tense or the present perfect tense depends on the time frame of the action. The time frame is usually established by an adverbial (e.g. immediately, after lunch, usually, today, etc.) The present perfect tense is used usually when the action started in the past and is continuing in the present. But if the action has clearly started and finished in the past, use simple past. E.g. I have jogged for 40 minutes already. (You started to 'jog' in the past but the 'already' implies you might still be doing the action) vs. I jogged for 1 hour yesterday morning. (You started to 'jog' and finished jogging in the past). You could also use it when the action just happened just recently. You would use simple past when the action happened further back in the past. E.g. I have completed all my homework just then. ('just then' is the adverbial that shows the time frame is recent). vs. I completed all my homework last week. ('last week' is the adverbial that shows the time frame is more in the past.) There are more examples but to answer your questions, the adverbial in your sentence is 'today'. 'Today' is a bit unique in that both simple past and present perfect tense can be used. Within 'today' there is plenty of time for both past simple and present perfect to be used. (e.g. I have studied hard today/ I studied hard today) You can use 'college has rejected you today' because 'today' hasn't ended yet and you are still rejected in the present. You can also use 'college rejected you today' because the action has happened in the distant past. Personally, I would use 'rejected' as it's implied that enough time has passed for the speaker to have heard the news and counsel their friend.

The same difference as in any of the questions about simple vs. perfect tenses you asked before: "have rejected" shows the importance of the fact that it has happened "up to now", "rejected" is just a fact in the past which is the only importance.

The first sentence is incorrect. Use of the Present Perfect 'has rejected' should not be followed with a time reference, in this case 'today'. Happy to give you a trial lesson on the subject :)