Field Bindweed

Convolvulus arvensis L.

Bindweed aka morning glory is one of the most invasive and hard to control weeds in the world. Most of the literature indicates that it is mildly toxic to livestock but then others list that sheep and hogs have been used to control it. Most of the feed lists for rabbits list it as toxic. However, studies have shown that deer and other wildlife use bindweed as a significant part of their diet. So, I smell bias.

My rabbits enjoy bindweed and I've been feeding it for years with no problems. Bindweed has deep roots that store protein and carbs which allow it to regrow quickly. I feed it fresh or dried.

Be warned that if it's in flower, you most likely will be spreading seed as the dry ones drop under the rabbit pen and mix with the manure or the seed goes right through your rabbit and stays viable. Unless you can get your compost very hot, there is a good chance some will survive to grow more rabbit feed when you spread it in your garden. That's true of many of the invasive plants I feed my rabbits. I've started using wood chips, leaves and grass clippings to heavily mulch my garden, so the problem is minimal. 

When I was a boy we called it morning glory. What a lovely name for a plant most gardeners loathe. I see a patch, smile then fill my bucket. More free greens to turn into meat that feeds my family.

References:
http://www.fs.fed.us/database/feis/plants/vine/conarv/all.html