It has been narrated from the Prophet ﷺ that he said: "The perfection of the prayer is the straightening of the row."(1)

And it has been narrated from ʿUmar that he used to appoint a man to straighten the rows, and he would not say the takbīr until he was informed that the rows had become level.(2)

And it has been narrated from ʿAlī and ʿUthmān that they both used to attend to this matter and would say: "Straighten yourselves."(3)

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(1) Recorded by Aḥmad (14454) from the ḥadīth of Jābir ibn ʿAbd Allāh.
And recorded by Aḥmad (12813), al-Bukhārī (723), Muslim (433), Abū Dāwūd (668), Ibn Mājah (993), and Ibn Ḥibbān (2171) and (2174) from the ḥadīth of Anas ibn Mālik with the wording: "Straighten your rows, for the straightening of the rows is part of the perfection of the prayer."

(2) This report from ʿUmar is authentic. It was recorded with a disconnected chain and a connected chain by Mālik in al-Muwaṭṭaʾ 1/158, ʿAbd al-Razzāq (2437–2439), and al-Bayhaqī 2/21.
And Ibn Abī Shaybah 1/352 recorded from Abū ʿUthmān al-Nahdī, who said: I was among those whom ʿUmar ibn al-Khaṭṭāb stationed before him for the straightening of the rows. Its chain is authentic.
And Ibn Abī Shaybah also recorded 1/352 from Abū ʿUthmān al-Nahdī, who said: I never saw anyone more attentive to the rows than ʿUmar. He would face the qiblah, and when we said, "He has said the takbīr," he would turn and look at the shoulders and feet. And he would send men to drive people until they joined them to the rows. Its chain is also authentic.

(3) The report from ʿUthmān concerning his attending to the rows and his command to straighten them is authentic. It was recorded by Mālik 1/158, ʿAbd al-Razzāq (2442), Ibn Abī Shaybah 1/352, and al-Bayhaqī 2/21–22, and in it: that ʿUthmān used to command the alignment of the rows, then he would not say the takbīr until the men he had appointed to straighten the rows came to him and informed him that they had become level, whereupon he would say the takbīr.
As for the report from ʿAlī, it was recorded by Ibn Abī Shaybah 1/352, and in its chain is Mujālid ibn Saʿīd, =