Can I call a stored procedure with hibernate criteria?

See Using stored procedures for querying in the reference documentation.

Mapped queries are called like this.

List employment = sess.getNamedQuery("BigSP")
    .list();

A mapped query can return entities.

<sql-query name="BigSP" callable="true">
    <return alias="emp" class="Employment">
        <return-property name="employee" column="EMPLOYEE"/>
        <return-property name="employer" column="EMPLOYER"/>
        <return-property name="startDate" column="STARTDATE"/>
        <return-property name="endDate" column="ENDDATE"/>
        <return-property name="regionCode" column="REGIONCODE"/>
        <return-property name="id" column="EID"/>
        <return-property name="salary">
            <return-column name="VALUE"/>
            <return-column name="CURRENCY"/>
        </return-property>
    </return>
    { call BigSP }
</sql-query>

No, you need to use a native query. If you are using annotations, see 2.3.2. Mapping native queries.

Below an example:

@Entity
@NamedNativeQuery(
    name="baz", 
    query="call fooProc(:bar, :i)", 
    callable=true, 
    readOnly=true, 
    resultClass=Foo.class
)
public class Foo {
    private Date when;
    //...
}

And to call it:

@Stateless
public class FooBean implements FooLocal {
    @PersistenceContext EntityManager em;

    public Foo getAFoo(string bar, int i) {
    Foo result = (Foo)em.createNamedQuery("baz").setParameter("bar", bar).setParameter("i", i).getSingleResult();
    return result;
    }

}

This document describes how to map the result of a stored procedure, executed as a native query.

You can't do it with the Criteria API, but this shouldn't matter.