Apache Connector というプラグイン？を使うらしい。

build.gradle

repositories {
    mavenCentral()
}

dependencies {
    compile 'org.glassfish.jersey.core:jersey-client:2.7'
    compile 'org.glassfish.jersey.connectors:jersey-apache-connector:2.7'
}

package sample;

import javax.ws.rs.client.Client;
import javax.ws.rs.client.ClientBuilder;
import javax.ws.rs.client.WebTarget;
import javax.ws.rs.core.MediaType;

import org.glassfish.jersey.apache.connector.ApacheConnectorProvider;
import org.glassfish.jersey.client.ClientConfig;
import org.glassfish.jersey.client.ClientProperties;

public class Sample {
    public static void main(String[] args) {
        ClientConfig config = new ClientConfig();
        config.connectorProvider(new ApacheConnectorProvider());

        config.property(ClientProperties.PROXY_URI, "http://proxy.host.name:8080"); // プロキシの URI
        config.property(ClientProperties.PROXY_USERNAME, "username");               // プロキシ認証のユーザー名（必要なら）
        config.property(ClientProperties.PROXY_PASSWORD, "password");               // プロキシ認証のパスワード（必要なら）

        Client client = ClientBuilder.newClient(config);

        WebTarget target = client.target("https://translate.google.co.jp")
                                 .path("translate_a/t")
                                 .queryParam("client", "t")
                                 .queryParam("ie", "UTF-8")
                                 .queryParam("oe", "UTF-8")
                                 .queryParam("sl", "en")
                                 .queryParam("tl", "jp")
                                 .queryParam("otf", "1")
                                 .queryParam("q", "Hello World.");

        String response = target.request(MediaType.APPLICATION_JSON_TYPE).get(String.class);
        System.out.println(response);
    }
}

実行結果

[[["世界こんにちは。","Hello World.","Sekai kon'nichiwa.",""]],,"en",,[["世界",[1],false,false,703,0,1,0],["こんにちは。",[2],false,false,658,1,3,0]],[["World",1,[["世界",703,false,false],["ワールド",296,false,false],["世界の",0,false,false],["の世界",0,false,false],["その他の",0,false,false]],[[6,11]],"Hello World."],["Hello .",2,[["こんにちは。",658,false,false]],[[0,5],[11,12]],""]],,,[["en"]],1]

JerseyClientでプロキシを通す方法

参考