Yes, although he didn’t simply give them up willingly.

By the time the crusade arrived in 1190, the Kingdom of Jerusalem had pretty much ceased to exist - the only part that Saladin never captured was the city of Tyre. The crusaders took back some territory, notably Acre in 1190 after a long siege, and Jaffa and the Egyptian fortress of Ascalon in 1191 after Richard defeated Saladin at the Battle of Arsuf.

For the next year there was a stalemate - Richard remained in the east, operating out of Jaffa, and knowing that as soon as he left Saladin would simply take back everything. Richard was also worried about his lands back home - he had already offended King Philip II of France, who left during the Siege of Acre and was now attacking Richard’s territories in France. On top of this, Richard fell ill during the summer of 1192 and wasn’t sure he would survive to see an end to the crusade.

So in August of 1192 Richard and Saladin began negotiating, with their messengers passing back and forth from Jaffa to Saladin’s camp outside the city. (Richard and Saladin never met in person.) Saladin wanted Ascalon back, and although Richard knew they would never get Jerusalem back through negotiation, he was able to demand other concessions in return for Ascalon. On September 2 they concluded a treaty, including a truce for three years and eight months, until April 1196.

This treaty basically recognized the status quo - the Kingdom of Jerusalem now comprised the Mediterranean coast from Jaffa in the south to Tyre in the north (in addition to the other crusader states in Tripoli and Antioch). The crusaders did have to return Ascalon though, but both sides agreed to dismantle it so it would no longer be useful for either side.

Saladin also kept Jerusalem itself, but pilgrims and merchants were allowed to visit and trade there. Many crusaders did end up making the pilgrimage to Jerusalem after the treaty was signed, although Richard himself never went.

Some of the crusaders were opposed to any sort of peace treaty, but at the same time it was getting harder for him to keep an army together if there was a stalemate and no action. He wanted to act quickly to end the crusade before it collapsed and Saladin retook everything. Saladin’s army also wanted to go home, and his advisors were also opposed because they believed this was just a stalling tactic, so Richard could return home and recruit more men and money.

In the end, Richard did return to Europe, but was taken prisoner by the Holy Roman Emperor along the way; his finances were ruined trying to pay his ransom, and he never returned to the east. Saladin also did not take advantage of Richard’s absence because he died not long after this in March 1193. The truce lasted until 1197, when a German crusade recaptured some territory for Jerusalem, notably Beirut.

(By the way, you might also see this treaty called the Treaty of Ramla, and to make it even more confusing, both names are sometimes also used for the treaty between Emperor Frederick II and Sultan al-Kamil in 1229.)

Sources:

Helen J. Nicholson, "Third Crusade", in The Crusades: An Encyclopedia, ed. Alan V. Murray (ABC-Clio, 2005)

M.C. Lyons, and D.E.P. Jackson, Saladin*: The Politics of the Holy War* (Cambridge University Press, 1982)

Helen J. Nicholson, trans., The Chronicle of the Third Crusade: The Itinerarium Peregrinorum et Gesta Regis Ricardi (Ashgate, 1997)

Baha' al-Din ibn Shaddad, The Rare and Excellent History of Saladin*, al-Nawadir al-Sultaniyya wa'l-Mahasin al-Yusufiyya*, trans. D. S. Richards (Ashgate, 2002)