I'm writing a little functional Interface and the method that it contains, takes an int as parameter. I was wondering if there's any way to check that when this method will be called, the value passed to the method, will not exceed a certain value and if it does, throw an error. Is there maybe an annotation I can add?

This is what my interface looks like

public interface DrawCardHandler{
    void onDrawCard(int slot);
} 

Define a class

Rather than pass around a mere int primitive, define a class to represent your specific meaning.

public final class Slot {
    private int value;
    public Slot(int value) {  // Constructor.
        if(/** your check goes here **/) {
            throw new IllegalArgumentException("...");
        }
        this.value = value;
     }
     // getter etc. goes here.
}

In Java 16 and later, use the records feature. A record is a brief way to write a class whose main purpose is to communicate data transparently and immutably. The compiler implicitly creates the constructor, getters, equals & hashCode, and toString. We can choose to write an explicit constructor to validate the input.

public record Slot (int value) {
    public Slot(int value) {  // Constructor.
        if(/** your check goes here **/) {
            throw new IllegalArgumentException("...");
        }
        this.value = value;
    }
    // The getters, equals & hashCode, and toString are implicitly created by compiler.
}

Then your interface could look like:

public interface DrawCardHandler{
    void onDrawCard(Slot slot);
} 

Define an enum

In general, if you know all possible slots in advance, you can create an enum for Slot instead of a class like I've shown - it will be even more expressive.