In src/main/webapp/WEB-INF/web.xml add:

<?xml version="1.0" encoding="UTF-8"?>
<web-app version="3.0" xmlns="http://java.sun.com/xml/ns/javaee" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://java.sun.com/xml/ns/javaee http://java.sun.com/xml/ns/javaee/web-app_3_0.xsd">

    <!-- ... -->

    <resource-env-ref>
        <resource-env-ref-name>BeanManager</resource-env-ref-name>
        <resource-env-ref-type>javax.enterprise.inject.spi.BeanManager</resource-env-ref-type>
    </resource-env-ref>
    <listener> 
        <listener-class>org.jboss.weld.environment.servlet.Listener</listener-class> 
    </listener>
</web-app>

In the pom.xml add:

<?xml version="1.0" encoding="UTF-8"?>
<project xmlns="http://maven.apache.org/POM/4.0.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd">

    <!-- ... -->

    <properties>
        <jersey.version>2.25</jersey.version>
    </properties>

    <dependencies>
        <dependency>
            <groupId>org.glassfish</groupId>
            <artifactId>javax.faces</artifactId>
            <version>2.2.8-02</version>
            <scope>runtime</scope>
        </dependency>
        <dependency>
            <groupId>org.jboss.weld.servlet</groupId>
            <artifactId>weld-servlet</artifactId>
            <version>2.3.4.Final</version>
        </dependency>
        <dependency>
            <groupId>org.glassfish.jersey.containers</groupId>
            <artifactId>jersey-container-servlet</artifactId>
            <version>${jersey.version}</version>
            <scope>runtime</scope>
        </dependency>
        <dependency>
            <groupId>org.glassfish.jersey.ext.cdi</groupId>
            <artifactId>jersey-cdi1x</artifactId>
            <version>${jersey.version}</version>
            <scope>runtime</scope>
        </dependency>
        <dependency>
            <groupId>org.glassfish.jersey.media</groupId>
            <artifactId>jersey-media-json-jackson</artifactId>
            <version>${jersey.version}</version>
            <scope>runtime</scope>
        </dependency>
        <dependency>
            <groupId>org.glassfish</groupId>
            <artifactId>javax.json</artifactId>
            <version>1.0.4</version>
            <scope>runtime</scope>
        </dependency>
        <dependency>
            <groupId>javax.servlet</groupId>
            <artifactId>jstl</artifactId>
            <version>1.1.2</version>
            <scope>runtime</scope>
        </dependency>
    </dependencies>
</project>

Create the file src/main/resources/META-INF/beans.xml with the following content:

<?xml version="1.0" encoding="UTF-8"?>
<beans
    xmlns="http://xmlns.jcp.org/xml/ns/javaee"
    xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
    xsi:schemaLocation="http://xmlns.jcp.org/xml/ns/javaee http://xmlns.jcp.org/xml/ns/javaee/beans_1_1.xsd"
    bean-discovery-mode="all">
</beans>

Create the file src/main/webapp/META-INF/context.xml with the following content:

<?xml version="1.0" encoding="UTF-8"?>
<Context path="/appName" swallowOutput="true">
    <Resource auth="Container" factory="org.jboss.weld.resources.ManagerObjectFactory" name="BeanManager" type="javax.enterprise.inject.spi.BeanManager"/>
</Context>