The story goes that Parashurama was sleeping with his head on Karna's lap. An insect started stinging Karna's thigh until blood was flowing and he bore the pain silently because he didn't want to wake his guru up.
When Parashurama woke up, he realized Karna could not be a Brahmin - only a Kshatriya can show that kind of tolerance for pain.
Yes, this story is mentioned in Mahabharata: Shanti Parva: Chapter 3:
Then Rama wrathfully addressed Karna, saying, 'O fool, no Brahmana could endure such agony. Thy patience is like that of a Kshatriya. Tell me the truth, without fear.' Thus asked, Karna, fearing to be cursed, and seeking to gratify him, said these words, 'O thou of Bhrigu's race, know me for a Suta, a race that has sprung from the intermixture of Brahmanas with Kshatriyas. People call me Karna the son of Radha.
Corresponding Sanskrit shlokas in Critical Edition Prepared by Scholars at BORI:
||१२ महाभारते शान्तिपर्वम् ||
राजधर्मपर्व
३
...
रामः कर्णं तु सक्रोधमिदं वचनमब्रवीत् ||२४||
अतिदुःखमिदं मूढ न जातु ब्राह्मणः सहेत् |
क्षत्रियस्यैव ते धैर्यं कामया सत्यमुच्यताम् ||२५||तमुवाच ततः कर्णः शापभीतः प्रसादयन् |
ब्रह्मक्षत्रान्तरे सूतं जातं मां विद्धि भार्गव ||२६||राधेयः कर्ण इति मां प्रवदन्ति जना भुवि |
प्रसादं कुरु मे ब्रह्मन्नस्त्रलुब्धस्य भार्गव ||२७||...
