"acquire access to" is correct and usable in written English.
You can use it to describe the act of gaining access to something, such as a place, document, or resource. For example: "The company recently acquired access to cutting-edge technology to improve their processes."
And China has made a major effort in recent years to acquire access to mineral and energy resources in many parts of the world.
Only after he dies does the former second-ranked bird, or beta male, move up in the hierarchy and acquire access to mates.
With some year-end funds and a substantial discount through our membership in CIFNAL, the Collaborative Initiative for French Language Collections, the Library was able to permanently acquire access to the Corpus Montaigne – our third database from Garnier Classiques Numérique.
The Media Institute, a nonprofit research foundation that focuses on communications policy, warned in its filing that the court's order could be "be applied against media companies as government authorities seek to acquire access to confidential information stored on mobile devices used by journalists".
Our job was to comb through the records of people who were in line to acquire access to secret information and make a first call about whether they should be allowed to have it, be investigated, or be shifted to less sensitive employment.
Although Kevin's objective in the attack was to acquire access to a network sniffer, his ultimate objective was to use it on DEC's own internal network (called EasyNet) to capture authentication credentials to access DEC's engineering network on which the proprietary source code for DEC's Virtual Memory System (VMS) operating system was stored.
By acquiring access to that information, an identity thief can impersonate someone else to commit fraud.
It is acquiring access to live travel data from air-traffic control systems.
The potential intruder has a vested interest in acquiring access to data in ways that will not readily make his presence known.
One way of acquiring access to such stories is through written literature (poetry, prose), which has survived centuries and is connected to specific landscapes.
The Associated Press reports: Moonves told reporters on a conference call that acquiring access to CNET's large online audience in order to distribute media content from CBS was "a large part" of CBS' motivation in going after the San Francisco-based online company.
