Do you have anything to read?

有~~东西用来做~~：英语是“have sth. to do”
这样的话很多，例如：

have sth. to drink:有~~可以喝
have sth. to eat:有~~可以吃

因为 have 本身就是动词呀，后面要是再接动词，中间就要放上一个 to.

want to do: 想做。

还有，do you have 不可以改成“have you”

因为 do you have 的肯定句是“i have”。have是动词，要用do 来问。
不过i have 还可以表示成“i have get”,所以你可以将 do you have 相应的改成“have you get”，这样句子就变成了：
Have you get anything to read?你有什么书可以看吗？

to read动词不定式修饰anything，have you不长用

to read动词不定式修饰anything

to read是动词不定式，在这里作“anything”的后置定语。

如果用have you，就成了Have you anything to read? 个人认为，这个句子也正确。