Update: This solution is no longer available; Punchfork has been acquired by Pinterest and will retire the API.
You can use the API offered by Food2Fork.
Food2Fork offers a similar api through which all of Allrecipes recipes are available.
You can also use Yummly’s API.
Yummly has indexed all of AllRecipe's recipes and have made them available through the Yummly Recipe API.
According to this Quora question, they don't, but most of their recipes are available through the Punchfork Recipe API.
And from Punchfork's API FAQ page:
Where do the recipes in the Punchfork API come from?
From popular food blogs and mainstream recipe sites around the web. See our full list of recipe publishing partners. We're constantly adding new sources to our database, and as we include more recipes, API users will automatically see the benefits in improved API results.
You will find allrecipes.com among their publishers.