Yes. Christians should place their faith into blood. Specifically, the blood of Jesus, our atoning sacrifice. You can see here that faith in Jesus is synonymous with faith in his blood for the atonement of sin:
Romans 3:23-26
23for all have sinned and fall short of the glory of God,
24and are
justified freely by His grace through the redemption that is in Christ Jesus.
25God presented Him as the atoning sacrifice
through faith in His blood, in order to demonstrate His righteousness, because in His forbearance He had passed over the sins committed beforehand.
26He did this to demonstrate His righteousness at the present time, so as to be just and
to justify the one who has faith in Jesus.
That's what it means to have faith in Jesus. You're having faith in his blood to atone for your sins. A person is justified and saved when they believe that the blood of Christ is the sacrifice for sin through which they are forgiven and reconciled to God. That's the good news of the gospel.
Acts 13:32-39
32And now
we proclaim to you the good news: What God promised our fathers
33He has fulfilled for us, their children, by raising up Jesus.
38T...
through Jesus the forgiveness of sins is proclaimed to you.
39Through Him
everyone who believes is justified from everything you could not be justified from by the law of Moses.