What is a “right hand servant”? Does the owner of a “right hand servant” have to be married?

Firstly: 

If Allaah enables the Muslim mujahideen to defeat kaafir enemies in war, then the men may be killed, ransomed, set free without ransom or enslaved. The choice between these four options is to be made by the ruler, according to what he thinks is the best course. 

With regard to the women, they become slaves and “those whom one’s right hand possesses” (described as a “right hand servant” in the question). Male children also become slaves. The ruler shares out these slaves among the mujaahideen. 

Shaykh al-Shanqeeti (may Allaah have mercy on him) said: The reason why a person may be taken as a slave is his being a kaafir and waging war against Allaah and His Messenger. If Allaah enables the Muslims who are striving and sacrificing their lives and their wealth and all that Allaah has given them to make the word of Allaah supreme over the kaafirs, then He allows them to enslave the kuffaar when they capture them, unless the ruler chooses to free them or to ransom them, if that serves the interests of the Muslims. 

Adwa’ al-Bayaan, 3/387 

Islam limited the sources of slaves which existed before the mission of the Prophet (peace and blessings of Allaah be upon him) to just one source, namely slavery resulting from capturing prisoners from among the kuffaar.  

Islam treated female slaves more kindly in their enslavement than other cultures did. Their honour was not considered to be permissible to anyone by way of prostitution, which was the fate of female prisoners of war in most cases. Rather Islam made them the property of their masters alone, and forbade anyone else to also have intercourse with them, even if that was his son. Islam made it their right to become free through a contract of manumission; it encouraged setting them free and promised reward for that. Islam made setting slaves free an obligation in the case of some kinds of expiation (kafaarah), such as the expiation for accidental killing, zihaar (a jaahili form of divorce in which a man said to his wife, “You are to me as my mother’s back”), and breaking oaths. They received the best treatment from their masters, as was enjoined by the pure sharee’ah. 

Secondly: 

A mujaahid does not have to be married in order to gain possession of a “slave whom one’s right hand possesses.” None of the scholars expressed such a view. 

Thirdly: 

If a mujaahid takes possession of a female slave or male slave, it is permissible for him to sell them. In either case – whether one acquires a slave through battle or through purchase – it is not permissible for a man to have intercourse with a female slave until she has had a period from which it may be ascertained that she is not pregnant. If she is pregnant then he must wait until she gives birth. 

It was narrated that Ruwayfi’ ibn Thaabit al-Ansaari said: I heard the Messenger of Allaah (peace and blessings of Allaah be upon him) say on the day of Hunayn: “It is not permissible for any man who believes in Allaah and the Last Day to irrigate the crop of another else – meaning to have intercourse with a woman who is pregnant. And it is not permissible for a man who believes in Allaah and the Last Day to have intercourse with a captured woman until he has established that she is not pregnant. And it is not permissible for a man who believes in Allaah and the Last Day to sell any booty until it has been shared out.” 

Narrated by Abu Dawood, 2158; classed as hasan by Shaykh al-Albaani in Saheeh Abi Dawood, 1890. 

For many reasons, including the fact that the Muslims have long since given up jihad, slavery is now very rare. This means that the Muslims must be extra cautious by examining any case in which it is claimed that someone is a slave, whether male or female. 

For more information see question no. 26067 

And Allaah knows best.