Download the tarball from julialang.org, then unpack it with tar into a directory of your choice. Then you can call the executable directly by path, or add the path to your PATH environment variable. For example,
gibson@sophist$ pwd
/home/gibson/tmp
gibson@sophist$ wget https://julialang-s3.julialang.org/bin/linux/x64/1.7/julia-1.7.0-linux-x86_64.tar.gz
--2021-12-09 16:49:37-- https://julialang-s3.julialang.org/bin/linux/x64/1.7/julia-1.7.0-linux-x86_64.tar.gz
Resolving julialang-s3.julialang.org (julialang-s3.julialang.org)... 151.101.130.49, 151.101.194.49, 151.101.2.49, ...
Connecting to julialang-s3.julialang.org (julialang-s3.julialang.org)|151.101.130.49|:443... connected.
HTTP request sent, awaiting response... 200 OK
Length: 123309942 (118M) [application/x-tar]
Saving to: ‘julia-1.7.0-linux-x86_64.tar.gz’
julia-1.7.0-linux-x86_64.tar.gz 100%[======================================================================>] 117.60M 8.57MB/s in 12s
2021-12-09 16:49:49 (10.1 MB/s) - ‘julia-1.7.0-linux-x86_64.tar.gz’ saved [123309942/123309942]
gibson@sophist$ tar xfpz julia-1.7.0-linux-x86_64.tar.gz
gibson@sophist$ ./julia-1.7.0/bin/julia
_
_ _ _(_)_ | Documentation: https://docs.julialang.org
(_) | (_) (_) |
_ _ _| |_ __ _ | Type "?" for help, "]?" for Pkg help.
| | | | | | |/ _` | |
| | |_| | | | (_| | | Version 1.7.0 (2021-11-30)
_/ |\__'_|_|_|\__'_| | Official https://julialang.org/ release
|__/ |
julia> 2+3
5