There is ... but you shouldn't be hitting it ... And if you ARE ... well, maybe a text file isn't what you're looking for.
Size wise, a file has different limitations depending on your file system ... NTFS (almost 16TB), FAT (fat 32 is almost 4GB), unix file systems will have their limitations, and so on ...
Like they suggest, your limit will be the size of the file.
As for your comment:
You can set the limit to whatever you wish.
What you do then is up to you ... if you decide to overwrite the file, it'll delete and start afresh. if you decide to append, it'll append to the end.
I would suggest create a queue of a 100 strings, and if you push new ones, drop the last one in the queue. Then you can just have that class save the log whenever, wherever and however you want.