Keep log file size fixed without logrotate

You could write a little bash script to do this. Just tail the file to a certain byte count using tail -c and overwrite the file.

from man tail:

-c, --bytes=N
              output the last N bytes; alternatively, use +N to  output  bytes
              starting with the Nth of each file

   If  the  first  character of N (the number of bytes or lines) is a `+',
   print beginning with the Nth item from the start of each  file,  other‐
   wise, print the last N items in the file.  N may have a multiplier suf‐
   fix:  b  512,  kB  1000,  K  1024,  MB  1000*1000,  M   1024*1024,   GB
   1000*1000*1000, G 1024*1024*1024, and so on for T, P, E, Z, Y.