Did St. Paul participate in the stoning of St. Stephen?

Yes, when he was a Pharisee

The Biblical record introduces Saul, who was later renamed Paul, as the “young man” at whose feet the false witnesses who stoned Christ’s disciple Stephen laid their outer garments. (Ac 6:13; 7:58) Paul approved of the murder of Stephen and, because of misdirected zeal for tradition, began a campaign of vicious persecution against Christ’s followers. When they were to be executed, he voted against them. At the time of their trial in synagogues, he endeavored to force them to recant. He extended his persecution to cities other than Jerusalem and even procured written authorization from the high priest to search out disciples of Christ as far N as Damascus, in Syria, and to bind them and bring them to Jerusalem, probably for trial by the Sanhedrin.—Ac 8:1, 3; 9:1, 2; 26:10, 11; Ga 1:13, 14.

As Paul neared Damascus, Christ Jesus revealed himself to Paul in a flashing light and commissioned him to be an attendant and a witness of the things he had seen and would yet see. Whereas those with Paul also fell to the ground because of this manifestation and heard the sound of someone speaking, Paul alone understood the words and was blinded, necessitating his being led by the hand to Damascus. (Ac 9:3-8; 22:6-11; 26:12-18) For three days he neither ate nor drank. Then, while praying in the house of a certain Judas at Damascus, Paul, in vision, saw Christ’s disciple Ananias come in and restore his sight. When the vision became reality, Paul was baptized, received holy spirit, partook of food, and gained strength.—Ac 9:9-19.

Information provide from the Article Paul, Insight on the scriptures.

http://m.wol.jw.org/en/wol/d/r1/lp-e/1200003406

He overlooked the stoning of Stephen, and continued to persecute Christians. But then Jesus came to him, and converted his heart and mind to do his will. This is in the book of Acts. You should read it, it's quite a good book.

the Bible does not say that saul participated in the actual stoning of Stephen, but does tell us that he stood by and watched and gave his approval.

yes, saul did persecute Christians and have them arrested and in some instances, killed.

Jesus came to him on the road to damascus and after that, he believed.

He supervised the stoning of Stephen and many other Christians.

I understand that this is the case. What made him convert? He had an epileptic fit.

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he was there to oversee the event . that was his job, to hunt down and deal with those who were involved in "the way."