The incident happened at Whiterock Hall in the Dunboyne Park area of the city last weekend.
A video has been posted online showing a man shimmying up the flag pole. It includes sectarian language. Police said the footage will form part of their investigation.
"On Wednesday 24 July, police received a report of the theft of a flag from an Orange Hall in the Dunboyne Park area of West Belfast sometime between Saturday 20 and Sunday 21 and are investigating," a PSNI spokesperson said.
"Police are aware of a video which has been posted on the internet and will examine this as part of the investigation along with any available CCTV footage."
On Thursday afternoon a man was arrested by police on suspicion of theft from the premises.
He is currently assisting police with their enquiries.
This community demands and is entitled to equality of respect, not to have its cultural identity violated.
William Humphrey, DUP MLA
Local DUP councillor Brian Kingston said the new flagpole had been erected just two weeks ago, in time for the Twelfth. He condemned the incident.
"I understand from the Hall Management Committee that the flag was stolen at around 5.25am last Saturday morning," Mr Kingson said.
"Clearly it was too much for some nationalists to tolerate that the Unionist community in west Belfast should be allowed to fly our national flag at an Orange Hall for a couple of weeks each summer.
"Last month this Hall was damaged in a sectarian arson attack when a wheelie bin was pushed against the back door and set on fire. These attacks will only strengthen the resolve of the Unionist community in the Highfield/Springfield area not to be cowed."
North Belfast DUP MLA William Humphrey also condemned the flag theft.
"The theft of the Union Flag and the posting of a video of this crime on social media were deliberately provocative acts, designed to increase inter-community tensions," the Orange Order member said.
He and other Orangemen met with PSNI on Thursday to highlight the attacks.
"It was useful to hold this meeting with the PSNI Area Commander regarding recent sectarian attacks on Whiterock Orange Hall and in the vicinity," he said.
"We also received updates on two recent sectarian attacks upon Whiterock Orange Hall.
"The PSNI Area Commander was able to confirm that one individual was arrested this afternoon and the police are continuing to seek other individuals."
He added: "In June the Hall was targeted in an arson attack which resulted in fire and smoke damage to the rear doorway and kitchen.
"Lodge officers passed evidential material to the police, including still photographs and CCTV footage relating to both attacks to assist with these ongoing investigations. The need for increased police patrols in the vicinity was communicated strongly."
Anyone with information has been asked to contact police on 0845 600 8000.