Reference: ad-Durar an-Naadhirah fil-Fataawa al-Mu’aasirah – Page 440
Question: If a poor and destitute person has not performed the obligatory hajj due to his financial inability to do so, in this case is it permissible to give him [funds] from the zakaah in order to facilitate his performing the obligatory hajj himself?
Response: There is no harm in giving the poor and destitute [funds] from the zakaah which will assist him in [performing] the hajj; And may Allaah grant everyone success.