Is it possible to install PHP7.4 on stock Alpine 3.12 Docker image?

Use alpine edge:

FROM alpine:edge
RUN apk add php
RUN php -v

This is update to Adiii answer suggesting to mix two alpine versions (3.12 and edge), this is terrible outcome, and difficult to understand what went wrong. You may end up with library errors, because it mixed one package from 3.12 and other package from edge:

/ # php -m
PHP Warning:  PHP Startup: Unable to load dynamic library 'igbinary.so' (tried: /usr/lib/php7/modules/igbinary.so (Error relocating /usr/lib/php7/modules/igbinary.so: php_error_docref0: symbol not found), /usr/lib/php7/modules/igbinary.so.so (Error loading shared library /usr/lib/php7/modules/igbinary.so.so: No such file or directory)) in Unknown on line 0 

You can use below Docker image.

FROM alpine:3.12
RUN apk add --no-cache  --repository http://dl-cdn.alpinelinux.org/alpine/edge/community php
RUN php -v

output

Step 3/3 : RUN php -v
 ---> Running in 9900e66f4b71
PHP 7.4.7 (cli) (built: Jun 14 2020 23:46:20) ( NTS )
Copyright (c) The PHP Group
Zend Engine v3.4.0, Copyright (c) Zend Technologies

If you want to see a full fledged example it's always best to investigate the vendor's Dockerfile.

This is from image php:7.4-fpm-alpine3.12:

https://github.com/docker-library/php/blob/86c8ec4d387132b65dbe6c5ab1747f858e03852e/7.4/alpine3.12/fpm/Dockerfile

As you can see, they add a lot of stuff to ensure PHP runs smooth and startup / context problems are solved.