Sahih al-Bukhari, Book 64, Hadith 226 (In-Book) ⓘ

Narrated Nafi`: The people used to say that Ibn `Umar had embraced Islam before `Umar. This is not true. What happened is that `Umar sent `Abdullah to bring his horse from an Ansari man so as to fight on it. At that time the people were giving the Pledge of allegiance to Allah's Messenger near the Tree, and `Umar was not aware of that. So `Abdullah (bin `Umar) gave the Pledge of Allegiance (to the Prophet) and went to take the horse and brought it to `Umar. While `Umar was putting on the armor to get ready for fighting, `Abdullah informed him that the people were giving the Pledge of allegiance to Allah's Apostle beneath the Tree. So `Umar set out and `Abdullah accompanied him till he gave the Pledge of allegiance to Allah's Messenger, and it was this event that made people say that Ibn `Umar had embraced Islam before `Umar.

حَدَّثَنِي شُجَاعُ بْنُ الْوَلِيدِ، سَمِعَ النَّضْرَ بْنَ مُحَمَّدٍ، حَدَّثَنَا صَخْرٌ، عَنْ نَافِعٍ، قَالَ إِنَّ النَّاسَ يَتَحَدَّثُونَ أَنَّ ابْنَ عُمَرَ، أَسْلَمَ قَبْلَ عُمَرَ، وَلَيْسَ كَذَلِكَ، وَلَكِنْ عُمَرُ يَوْمَ الْحُدَيْبِيَةِ أَرْسَلَ عَبْدَ اللَّهِ إِلَى فَرَسٍ لَهُ عِنْدَ رَجُلٍ مِنَ الأَنْصَارِ يَأْتِي بِهِ لِيُقَاتِلَ عَلَيْهِ، وَرَسُولُ اللَّهِ صلى الله عليه وسلم يُبَايِعُ عِنْدَ الشَّجَرَةِ، وَعُمَرُ لاَ يَدْرِي بِذَلِكَ، فَبَايَعَهُ عَبْدُ اللَّهِ، ثُمَّ ذَهَبَ إِلَى الْفَرَسِ، فَجَاءَ بِهِ إِلَى عُمَرَ، وَعُمَرُ يَسْتَلْئِمُ لِلْقِتَالِ، فَأَخْبَرَهُ أَنَّ رَسُولَ اللَّهِ صلى الله عليه وسلم يُبَايِعُ تَحْتَ الشَّجَرَةِ ـ قَالَ ـ فَانْطَلَقَ فَذَهَبَ مَعَهُ حَتَّى بَايَعَ رَسُولَ اللَّهِ صلى الله عليه وسلم، فَهِيَ الَّتِي يَتَحَدَّثُ النَّاسُ أَنَّ ابْنَ عُمَرَ أَسْلَمَ قَبْلَ عُمَرَ‏.‏