Is there a way to get a history of transaction log used space in SQL Server?
Nothing is logged by default, generally speaking. So, unless you have something keeping track of the amount of log generated, you are out of luck. 

Ordinarily, we would recommend you to check the size of your log backups, but as I understand it, you don't have those and the purpose here is to determine how much space you would need for those. Catch 22. :-)

Even with some active monitoring, you would have to check this pretty frequently, since you never know when checkpoint kicks in and "truncate the log". There's a perfmon counter you can use for this: "Log File(s) Used Size (KB)". And you can grab the value from sys.dm_os_performance_counters. I.e., pretty easy to create a job that uses a SELECT to check the used space in the tlog for selected databases, store it in a table and execute that job every minute, or whatever frequency you find suitable.