اللَّهُمَّ رَبَّ هَذِهِ الدَّعْوَةِ التَّامَّةِ وَالصَّلَاةِ الْقَائِمَةِ آتِ مُحَمَّدًا الْوَسِيلَةَ وَالْفَضِيلَةَ وَابْعَثْهُ مَقَامًا مَحْمُودًا الَّذِي وَعَدْتَهُ
Transliteration
Allahumma Rabba hadhihid-da'watit-tammati was-salatil-qa'imati ati Muhammadan al-wasilata wal-fadilata wab'athhu maqaman mahmudan alladhi wa'adtah
English meaning
O Allah, Lord of this perfect call and of the prayer about to be established, grant Muhammad the wasilah and the virtue, and raise him to the praiseworthy station that You have promised him.
When is it recited?
Recited quietly after listening to the adhan. Sending salawat upon the Prophet after the adhan is sunnah, and reciting this supplication is recommended (mustahab).
Its virtue
The Prophet (PBUH) said that whoever says this when hearing the call to prayer will be entitled to his intercession on the Day of Resurrection.
Source
Bukhari, Adhan 8, 614