Sayyiduna Anas Ibn Malik (radiyallahu’anhu) reports that Rasulullah (sallallahu ‘alayhi wa sallam ) would recite the following supplication when the Month of Rajab would commence:
ﺍَﻟﻠّٰﻬُﻢَّ ﺑَﺎﺭِﻙْ ﻟَﻨﺎَ ﻓِﻲْ ﺭَﺟَﺐٍ ﻭَﺷَﻌْﺒﺎﻥَ ﻭَﺑَﻠّﻐْﻨَﺎ ﺭَﻣَﻀَﺎﻥْ
Allahumma baarik lana fi Rajaba wa Sha’bana wa balligh-na Ramadan
Translation: Oh Allah! Grant us Barakah (Blessing) during (the months of) Rajab and Sha’ban, and allow us to reach Ramadan.
(Shu’abul-Iman, Hadith: 3534, Ibnu Sunni, Hadith: 660, Mukhtasar Zawaid Bazzar, Hadith: 662, also see Al-Adhkar, Hadith: 549)