The crackdown began last month when Turkish ISPs were told to cut off the virtual private networks people use to hide where they go.
Many people are changing the way they connect to Tor to avoid the block.
Activists said the block moved Turkey's net censorship policies from "moderate" to "severe".
Tor, also known as The Onion Router, aims to conceal where people go online by using encryption and randomly bouncing requests for webpages through a network of different computers.
The system has become popular in many nations, such as China and Turkey, where governments are known to watch what people do and say online.
Now Turkey Blocks, which monitors internet censorship in the nation, said its regular monitoring of Tor showed that it was being widely blocked across the country.
The organisation started to investigate after many people in Turkey reported having problems reaching the Tor network.
It added that the Turkish government had put in place sophisticated systems at ISPs to spot when people were trying to connect to Tor.
These inspect packets of data and can pick out the distinctive signature of those that are destined for Tor.
Turkey Blocks said the Turkish government ordered firms to start blocking VPNs and Tor in early December, and has increased the pressure on firms to act by asking for weekly updates about the success of the measures.
The monitoring group said that while direct access to Tor was not working well, many people were reporting that they could still access the network if they used a bridge.
These are unofficial entry points to the Tor network which, because they are not listed in the software itself, can survive when blocks are imposed.
Turkey has a long history of cutting off access to websites and services - particularly during periods of social unrest.

Police Scotland were called to investigate at the end of June when Annan Athletic failed to receive an end of season payment from the league.
The League Two side were expecting about £18,000 but the funds were paid into a fraudulent account.
BBC Scotland has learned that the money has been retrieved and that the police investigation continues.
The SPFL said it has been subject to further attempts at hacking and fraudulent activity as recently as this week.

The device was found at Corfe Mullen, Dorset on Tuesday morning.
A Military Explosive Ordnance Disposal team (EOD) has set up a 1,000m (0.62 mile) exclusion zone at Henbury Quarry in Old Market Road, ahead of a controlled explosion at 10:00 GMT.
Local roads within the cordon and the A350 will be closed from 09:30.
Superintendent Caroline Naughton, of Dorset Police, said: "I would like to reassure residents that there is no immediate risk to anyone in the local area.
"When the controlled explosion takes place it is anticipated that a loud bang will be heard in the area."
A rest centre has been set up for residents at the Memorial Hall, Sturminster Marshall.
People are being urged to take any pets or medication with them.
Dorset Police said staff and pupils from Castle Court School are being taken to another site.
The cordon is expected to be lifted by 11:00 GMT.

The fire blew out the windows of the property on Lewes Road, initially leading to reports that there had been an explosion.
Emergency services attended the scene at 02:50 BST and the body was discovered in the upstairs of the house, which had been badly damaged.
Police and the fire service are carrying out a joint investigation into the cause of the fire.
Residents from several neighbouring homes, which were evacuated, have now been allowed back into their properties.
The street, just off Neasham Road, remains cordoned off.

The officer was carrying a handgun in the railway station in Inverness on Tuesday as he walked through the main concourse.
Police Scotland said the officer had breached new force policy.
A spokesman said he had been reminded of the strict criteria about the issue.
It was a sight more common in 2013 when a policy was introduced allowing firearms officers to carry handguns with them at all times while on duty.
However, after concerns from politicians, the chief constable of Police Scotland, Sir Stephen House, stated last October that specialist armed police officers in Scotland would only be deployed to firearms incidents or where there was a threat to life.
Turkey has blocked direct access to the Tor anonymous browsing network as part of a wider crackdown on the ways people circumvent internet censorship.
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The Scottish Professional Football League is warning clubs to be on their guard against online fraud.
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