I dont know how to do it with ASP.NET Core, but as mentioned in below docs you should be able to do that at ingress level.
Kubernetes ingress
There is documentation about that in kubernetes ingress.
Rate limiting
These annotations define limits on connections and transmission rates. These can be used to mitigate DDoS Attacks.
nginx.ingress.kubernetes.io/limit-connections: number of concurrent connections allowed from a single IP address. A 503 error is returned when exceeding this limit.
nginx.ingress.kubernetes.io/limit-rps: number of requests accepted from a given IP each second. The burst limit is set to 5 times the limit. When clients exceed this limit, limit-req-status-code default: 503 is returned.
nginx.ingress.kubernetes.io/limit-rpm: number of requests accepted from a given IP each minute. The burst limit is set to 5 times the limit. When clients exceed this limit, limit-req-status-code default: 503 is returned.
nginx.ingress.kubernetes.io/limit-rate-after: initial number of kilobytes after which the further transmission of a response to a given connection will be rate limited. This feature must be used with proxy-buffering enabled.
nginx.ingress.kubernetes.io/limit-rate: number of kilobytes per second allowed to send to a given connection. The zero value disables rate limiting. This feature must be used with proxy-buffering enabled.
nginx.ingress.kubernetes.io/limit-whitelist: client IP source ranges to be excluded from rate-limiting. The value is a comma separated list of CIDRs.
If you specify multiple annotations in a single Ingress rule, limits are applied in the order limit-connections, limit-rpm, limit-rps.
To configure settings globally for all Ingress rules, the limit-rate-after and limit-rate values may be set in the NGINX ConfigMap. The value set in an Ingress annotation will override the global setting.
The client IP address will be set based on the use of PROXY protocol or from the X-Forwarded-For header value when use-forwarded-headers is enabled.
There is medium tutorial about Rate-limiting for your Kubernetes applications with kubernetes ingress.
Nginx ingress
There is documentation about that in nginx ingress.
If you're confused why I mentioned both kubernetes and nginx ingress, take a look here
There are two popular Kubernetes Ingress controllers that use NGINX – both are open source and hosted on GitHub. One is maintained by the Kubernetes open source community (kubernetes/ingress-nginx on GitHub) and one is maintained by NGINX, Inc. (nginxinc/kubernetes-ingress on GitHub)
Hope you find this useful.