Assuming this process is run once a day and you want current day plus last 90 days, give this a try:

declare @BatchSize int = 10000,

@CurrentDate date = getdate(),

@KeepDays int = 90;

while @BatchSize > 0

begin

delete top (@BatchSize)

from dbo.ServiceLog

where

Created < dateadd(day,-(@KeepDays),@CurrentDate);

set @BatchSize = @@ROWCOUNT;

end