You can even say it's worth a try, which is probably the usage I personally would opt for.
There is a difference in semantics between being worth something and deserving something, but notwithstanding the semantically different “angle”, they are often, like in these expressions, interchangeable.
To be worth something means that something represents a certain value. Literally, as in this house is worth a lot of money, or figuratively, as in this book is worth reading.
It means that if you were to invest something (time, effort, money) in exchange for the object, you would have a good deal.
To deserve something means that something or someone has the right to receive something — either because of inherent qualities or because of a delivered good or effort. Literally, as in an employee deserves to be paid for doing their work or figuratively as in this book deserves reading.
As you noticed, when I am talking about a good book, I can use both options without any problem. For some people, there might be a small perceived difference in meaning, but I dare say that in general, both options will be interpreted the same.
On the other hand, these examples would not sit well with most people:
This house deserves a lot of money.
It raises the question what the house did to "deserve" money. The sentence indicates I should give money to the house, not to buy it, but because somehow the house deserves to be donated funds.
An employee is worth money for their job.
This treats the employee as a commodity, that can be bought!
In general, deserve indicates some (moral) right to something, whereas worth indicates a real of figurative value.
Crime deserves punishment. (not is worth punishment!)
This painting is worth a fortune. (not deserves a fortune!)