Dua in The Month of Rajab

Rajab was regarded as one of the sacred months (Al-Ashhur-al-hurum) in which battles were prohibited in the days of the Holy Prophet . It is also a prelude to the month of Ramadan, because Ramadan follows it after the intervening month of Sha'ban. Therefore, when the Holy Prophet sighted the moon of Rajab, he used to pray to Allah in the following words:

  اللَّهُمَّ بَارِكْ لَنَا فِي رَجَبٍ، وَشَعْبَانَ، وَبَلِّغْنَا رَمَضَانَ

"O Allah, make the months of Rajab and Sha'ban blessed for us, and let us reach the month of Ramadan (i.e. prolong our life up to Ramadan, so that we may benefit from its merits and blessings)."

The chain of Hadith is dhaeef. 

Note: Making dua with the words of Dhaeef hadith is better than making dua in your own words. 

Specific Worships for the month of Rajab  

The Shari'ah has not prescribed any specific way to observe the month of Rajab or to perform a specific mode of worship or a ritual in any one of its dates. However, being a prologue to the month of Ramadan, it should be availed of for preparing oneself for Ramadan and one should pray Allah to make him reach the blessed month and to benefit from its unique merits.

Some people have invented some special rituals or practices in this month, which are not supported by reliable resources of the Shari'ah or are based on some unauthentic traditions.

https://gatewaytoquran.weebly.com