Nicola Sturgeon revealed on November 30 that the one-off, pro rata payment for health and social care staff would be paid out – and urged the UK government to lift it out of taxation.
However, an email to Mr Rennie from Fife Council has said that it is unlikely to be paid out before May.
The council wrote: "As councils are only administrators of the payment, separate funding is needed from the Scottish Government. That is unlikely to be in place until early April. That being the case it is unlikely that Fife Council will be able to make payments until the end of that month or more realistically the May pay."
Mr Rennie said: "We are very fortunate that council social care staff are significantly more efficient at caring for people than the Scottish Government are at getting bonuses into bank accounts. Six months is an awfully long time to wait.
“Social care staff have been saving SNP ministers' blushes for too long by continually going above and beyond the call of duty. That deserves proper recognition and the setting of new fair work standards across the entire sector."
A Scottish Government spokesperson said: “This claim is wrong – working with COSLA, we are on track for payments to be made to local authorities from the end of March as scheduled. This timeline was set out by the Scottish Government in December.”