Yep, spray with Roundup to kill everything off. Start fresh.
Rotovate after a couple of weeks and if the soil is good just spread and level your topsoil and sow your grass. Keep the grass seed moist until it shows. You'll have a nice grassy garden by the end of the Summer, if it ever comes.
Edit, just noticed you have an acre. Yikes, not as easy as it sounds above.
I did the same area last June but because of the work load I got someone in with the right equipment (excavator, dumper, stone picker, harrow, seed spreader etc) to do it.
And yes, when it's done, you will spend half of every weekend mowing the bloody thing.