I've run is the only correct answer. Ran is not used with auxiliary verbs. Run is an irregular verb. I run, I ran, I have run Ran is simple past. I run to the store. I am running to the store. (I am in the process of doing it right now.) I ran to the store yesterday. (I did it and the action is completed.) I have run to the store means that it happened in the past but the action is not necessarily completed or there is something conditional about the action. You might leave a note for your mother saying "I have run to the store" and to explain your absence from the house. The implication is that you will return. Run can mean caminhar or literally correr. I ran a marathon. A one-time event that is completed. I have run a marathon. I have done it in the past and I may or may not do it in the future. Or, to emphasize that you have been capable of doing it.

“I’ve run.”is the correct one. “have/has done” we need to use past participle here.

Present: run Past: ran Past participle: run Correct: I've run

Ran